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Subject and Purpose. The effects considered concern phase synchronization of electrons in an ideal plasma subjected to the action of an external uniform, d. c. magnetic field. Two modes of the synchronization are discussed, specifically one by an external electromagnetic field and the other by the cyclotron radiation emitted by the electrons. The purpose is to compare these forms of synchronization and their effects on plasma stability. Methods and Methodology. The plasma is represented as a set of coupled oscillators whose dynamics is described via coupled differential equations. Assuming the coupling between the oscillators to be weak we find analytical solutions to the equation, further performing a stability analysis which exploits standard approaches of the dynamical systems theory. The solutions found are validated through corresponding numerical simulations. Results. As has been found, an external electromagnetic wave may be capable of guiding the particles toward phase synchronization, which can lead to formation of phased bunches. This mechanism of particle grouping may prove to be more efficient, in terms of scale times of synchronization, if compared with known mechanisms exploiting relativistic effects. Additionally, we show that the cyclotron radiation emitted by the charged particles (which is often disregarded because of its smallness) can lead to self-phase synchronization of the electrons. Moreover, should the density of charged particles in the ensemble be sufficiently high, an instability can arise, potentially disrupting the ensemble. Estimates have been provided of the level of random fluctuations capable of undermining the synchronization process and plasma dynamics stabilization. Conclusions. The most significant finding of this analysis is the emergence of low-frequency oscillations in the charged oscillators set, followed by an onset of the plasma instability when the plasma density exceeds a certain critical value. Within that scenario, the ensemble of oscillators sitting in the external magnetic field is no longer held together by the field. The effect should be taken into account in applications related to plasmas of a relatively high density.

Aim of this work is to develop the theory of mutual synchronization of two oscillators with hard excitation associated with a delay. Taking into account the delay of a coupling signal is necessary, in particular, when analyzing synchronization at microwave frequencies, when the distance between the oscillators is large compared to the wavelength. Methods. A bifurcation analysis of the mutual synchronization of two generators with hard excitation in the amplitude-phase approximation is carried out. The results of the bifurcation analysis are compared with the results of numerical simulation of the system of differential equations with delay. Results. A complete bifurcation pattern of mutual synchronization on the plane “frequency mismatch — coupling parameter” is presented. In the case of small mismatch and weak coupling, the fixed points, which correspond to modes with dominance of one of the oscillators, merge with saddle fixed points and disappear when the coupling parameter increases. In the case of large mismatch, one of these points either vanishes or loses stability as a result of a subcritical Andronov–Hopf bifurcation. The other of these points remains stable at any values of the coupling parameter, and the oscillation amplitudes of both oscillators gradually equalize and the phase difference tends to zero, i.e., the oscillation mode with dominance of one of the oscillators gradually transforms into the in-phase synchronization mode. It has been found that with an increase in the coupling parameter, a transformation of the basin of attraction of a stable zero fixed point occurs. As a result of this transformation, if at the initial moment of time the oscillations of the generators are close to antiphase, the oscillations decay at any initial amplitudes. Conclusion. The synchronization pattern in the system of delay-coupled oscillators with hard excitation has been studied. It was discovered that in addition to mutual synchronization modes with approximately equal oscillation amplitudes, stationary modes with suppression of oscillations of one generator by another are also possible. The bifurcation mechanisms of the appearance and disappearance of multistability in the system have been examined.

The relevance of the topic of this study is due to the need to ensure reliable operation of vehicles and minimize the risks of interruptions in the operation of internal combustion engines (ICE). A common phenomenon in operation is misfiring, which negatively affects the efficiency of the ICE and can lead to emergencies that entail significant financial and temporary losses for commercial companies. The problem is the need to identify and prevent such malfunctions early. The purpose of the study is to develop and test a system for monitoring and analyzing the technical condition of the internal combustion engine through vibration measurements. Method and methodology. The work used the method of in-place diagnostics, the use of which increases efficiency of determining the technical condition of the vehicle internal combustion engine. Results. This article describes the system developed by the authors for checking the technical condition of an internal combustion engine. As a result, software to process and record vibration and timing data has been developed in MATLAB. The study of influence of defects in mechanisms and systems of internal combustion engine on uniformity of time-amplitude characteristic of vibration pulses of each individual cylinder, which occur during operation of internal combustion engine, was carried out by calculation and experimentation. As a key conclusion, it is noted that the developed system allows to quickly and non-invasively identify the idle cylinder or the one of which contribution to the rotational movement of the crankshaft is the least compared to others. The research makes it possible to provide diagnostics in a short time using available means. Scope of application of the results. the research results were tested in the conditions of a service company when diagnosing the internal combustion engines of passenger cars and trucks, and can be applied by both car repair shops and car enthusiasts.

dynamics of power relations and resistance. It draws on the concept of multitemporality, which posits that different 'temporal regimes' — different experiences of time and different temporal constructions of past, present, and future — can coexist. Drawing on the work of K. Mannheim, H. Rosa, and M. Foucault, the article illustrates that power and resistance operate in different temporal regimes, perceive social change at different speeds, and have different attitudes towards the past and the future. The article explores how the optics of multitemporality can serve resistance politics and have an emancipatory effect. Using Foucault's concepts of power and resistance, it describes specific multitemporal characteristics associated with power and resistance, such as power's tendency to slow down the passage of time and resistance's struggle against the determination of the future. The article considers how the temporal aspect helps power to maintain and strengthen its dominance, while enabling resistance to create alternative future scenarios. It emphasizes that resistance acts as a catalyst for social change and, drawing on the ideas of Foucault and Deleuze, underlines the primacy of resistance over power. It concludes that resistance not only seeks to outpace power in time, but represents a qualitatively different approach to time and history.

Aim of this work is to develop the theory of mutual synchronization of two oscillators with hard excitation associated with a delay. Taking into account the delay of a coupling signal is necessary, in particular, when analyzing synchronization at microwave frequencies, when the distance between the oscillators is large compared to the wavelength. Methods. Theoretical analysis is carried out under the assumption that the delay time is small compared to the characteristic time for the oscillations. The phase approximation is used when the frequency mismatch and the coupling parameter are considered small. Results. Taking into account the change in oscillation amplitudes up to first-order terms in the coupling parameter, a generalized Adler equation for the phase difference of the oscillators is obtained, which takes into account the combined type of the coupling (dissipative and conservative coupling) and non-isochronism. The conditions for saddle-node bifurcations are found and the stability of various fixed points of the system is analyzed. The boundaries of the domains of in-phase and anti-phase synchronization are plotted on the plane of the parameters “frequency mismatch – coupling parameter”. Conclusion. It is shown that, depending on the control parameters (non-isochronism parameter, excitation parameter, phase advance of the coupling signal), the system exhibits behavior typical of either dissipative or conservative coupling. The obtained formulas allow for trace the transition from one type of coupling to another when varying the control parameters.

According to the stick-slip model, the relative movement of the fault planes is an act of unstable sliding, where movement begins when the stresses tangential to the fault plane reach a certain limit. The physical mechanism of dynamic slip along a fault consists of the sequential formation of conglomerates of loaded particles (force chains) in the contact zone and their subsequent destruction. These chains together form a force skeleton characterized by a specific spatial structure and strength properties. An increase in shear stress on the fault banks leads to local destruction of the strength skeleton; further evolution of the system brings destruction processes to higher spatial levels, ultimately leading to a shift in the fault banks. Since the evolution of the process of destruction of force chains in the contact zone of a fault along the hierarchy of scales from bottom to top is similar to the evolution of crack formation in a loaded medium from microscale to macroscale (specimen scale), the authors hypothesized the coherent behavior of acoustic noise accompanying the preparation of dynamic slip and recorded in different areas of fault zones. This work is devoted to testing this hypothesis on a laboratory scale, using an installation that simulates movement along a fault. As a result of the analysis, the hypothesis about the synchronization of the statistical properties of the acoustic emission during the preparation and implementation of the dynamic movement was confirmed. It is shown that the observation (detection) of the effect of the synchronization of the statistical properties of acoustic emission depends both on the set of parameters for which the spectral coherence measure is calculated and on the location of the recording of the initial data.

The purpose of this study was to develop a mathematical model of the photoplethysmogram, which can be used to test methods that introduce the instantaneous phases of the modulating signals. The model must reproduce statistical and spectral characteristics of the real photoplethysmogram, and explicitly incorporate the instantaneous phases of the modulating signals, so they can be used as a reference during testing. Methods. Anacrotic and catacrotic phases of the photoplethysmogram pulse wave were modeled as a sum of two density distributions for the skew normal distribution. The modulating signals were introduced as harmonic functions taken from the experimental instantaneous phases of the VLF (0.015...0.04 Hz), LF (0.04...0.15 Hz) and HF (0.15...0.4 Hz) oscillations in the real photoplethysmogram. The spectral power in the VLF, LF, and HF frequency ranges was calculated to compare the model and experimental data. Results. The model qualitatively reproduces the shape of the experimental photoplethysmogram pulse wave and shows less than 1% error when simulating the spectral properties of the signal. Conclusion. The proposed mathematical model can be used to test the methods for introduction of the instantaneous phases of the modulating signals in photoplethysmogram time-series.

Purpose of this work is the research of the dynamical processes and in particular the phenomenon of the synchronization in an ensemble of coupled chaotic economic oscillators. Methods. The research methods are the qualitative and numerical methods of the theory of nonlinear dynamical systems and the theory of the bifurcations. Results. The nonlinear model of economic oscillator as the system of automatic control are considered. Such kind of general economic models are unsuitable for getting some concrete economic estimations and recommendations. But such kind models are very useful for a development the theory of the economic cycles, theory of the generation, interactions, synchronization of the cycles and so on. Our numerical experiments demonstrated a good enough qualitative similarity of an chaotic economic oscillations in our model and real economic cycles. The phenomen of the synchronization of the chaotic oscillations in the ensemble of coupled economic oscillators are considered, however the accuracy of the synchronization depends with couplings essentially.

The purpose is to study the periodic regimes of the dynamics for two non-identical predator–prey communities coupled by migrations, associated with the partial synchronization of fluctuations in the abundance of communities. The combination of fluctuations in neighboring sites leads to the regimes that include both fast bursts (bursting oscillations) and slow oscillations (tonic spiking). These types of activity are characterized by a different ratio of synchronous and non-synchronous dynamics of communities in certain periods of time. In this paper, we describe scenarios of the transition between different types of burst activity. These types of dynamics differ from each other not so much in size, shape, and number of spikes in a burst, but in the order of these bursts relative to the slow-fast cycle. Methods. To study the proposed model, we use the bifurcation analysis methods of dynamic systems, as well as geometric methods based on the division of the full system into fast and slow equations (subsystems). Results. We showed that the dynamics of the first subsystem with a slow-fast limit cycle directly determines the dynamics of the second one with burst activity through a smooth dependence of regime on the number of predators and a non-smooth dependence on the number of prey. We constructed the invariant manifolds on which there are parts of dynamics with tonic (slow manifold) and burst (fast manifold) activity of the full system. Conclusion. We described the scenario for bursting with different waveforms, which are determined by the appearance of the fast invariant manifold and the location of its parts relative to the slow-fast cycle. The transitions between different types of burst are accompanied by a change in the oscillation period, the degree of synchronization, and, as a result, the dynamics becomes quasi-periodic when both communities are not synchronous with each other.

Purpose of the work is to research of the world science publications dynamics on the synchronization. Methods. The research methods are the statistical methods of data processing. Results. The emphasis in the study of synchronization over the past twenty years has shifted from physical and technical sciences to neuroscience with Asian countries domination.

The paper is devoted to development of atypical excitation approaches of bistatic laser monitor active elements for the imaging of high-speed processes at a powerful background radiation. The practical significance is increasing the temporal resolution of the bistatic laser monitor, as well as improving the imaging parameters by minimizing the jitter of radiation pulses. To achieve this goal, semiconductor excitation sources of active media based on copper bromide vapor were developed, and their synchronization was performed in a pulse-repetition mode. The developed pump sources are set of identical commutation cells. Each cell contains storage capacitor, commutator and transformer. Powerful HGTG27N120BN insulated-gate bipolar transistors (IGBT) were chosen as commutators. Their switching storage capacitors are discharged through the primary winding of the transformer and as result the voltage pulse is induced in the secondary winding. The transformer load was the gas discharge tube (GDT) of the small-size brightness amplifier with the specified geometric parameters (l = 40 cm, d = 2.5 cm, V = 196 cm3). The simultaneous switching of 10 identical cells provided GDT breakdown. The radiation power of the active element in oscillator mode was 665 mW. The developed brightness amplifier with semiconductor pump source was used in the bistatic scheme of the laser monitor for the imaging of the test object. The pumping of the second active element, the illumination source (l = 90 cm, d = 5 cm, V = 1767 cm3), was performed by means of thyratron TGI1-1000-25. The pulse repetition frequency of the illumination source and the brightness amplifier was 10.5 and 21 kHz respectively. As result each second image was formed with increased brightness and contrast. The maximal jitter of radiation pulses in this case was 16 ns. The average jitter was 6 ns. Two identical semiconductor pump sources were tested simultaneously. The resulting array of waveforms (GDT current and GDT voltage) show that in most cases the jitter was completely absent, and when it appeared, it did not exceed 4 ns. The imaging at this configuration of the pump sources was not performed due to semiconductor source power (465 W) turned out to be insufficient for the excitation of the illumination source, and therefore options for increasing it were proposed. [ABSTRACT FROM AUTHOR]

The purpose of this work is to study the possibility of synchronization of wave processes in distributed excitable systems by means of noise modulation of the coupling strength between them. Methods. A simple model of a neural network, which consists of two coupled layers of excitable FitzHugh–Nagumo oscillators with a ring topology, is studied by numerical simulation methods. The connection between the layers has a random component, which is set for each pair of coupled oscillators by independent sources of colored Gaussian noise. Results. The possibility to obtain a regime close to full (in-phase) synchronization of traveling waves in the case of identical interacting layers and a regime of synchronization of wave propagation velocities in the case of non-identical layers differing in the values of the coefficients of intra-layer coupling is shown for certain values of parameters of coupling noise (intensity and correlation time). Conclusion. It is shown that the effects of synchronization of phases and propagation velocities of excitation waves in ensembles of neurons can be controlled using random processes of interaction of excitable oscillators set by statistically independent noise sources. In this case, both the noise intensity and its correlation time can serve as control parameters. The results obtained on a simple model can be quite general.

Purpose of this work is studying of the dynamics of a power grid model that results from the expansion of a highly centralized grid, i.e. a hub-cluster, by adding a small subgrid. The main attention is paid to the study of possible power grid operation regimes and their characteristics. Methods. Numerical simulation of power grid operation, the dynamics of which is described by the Kuramoto equations with inertia, is used. Results. Various power grid operation regimes and the boundaries of their existence in the parameter space are given. The main characteristics of these regimes, such as the probability of realization and the magnitude of oscillations of regime variables, are considered. The conditions for safe connection to hub-cluster power grids are obtained. Conclusion. The dynamics of power grid consisting of two subgrids and its operation regimes are considered. Based on the characteristics of these regimes, their safety for subgrids is determined. The results obtained made it possible to formulate conditions for a safe connection to hub-cluster power grids.

Purpose of this work is to determine regularities of formation of spatial structures in an ensemble of chaotic systems with non-local diffusion couplings and to study how these structures depend on the wave response of the digital filter formed by the ensemble couplings structure. Methods. The study was carried out by numerical simulation of an ensemble of logistic maps, calculation of its typical oscillatory regimes and their spectral analysis. The network was considered as a digital filter with a frequency response depending on the coupling parameters. Correlation between the spatial spectra and the amplitude-frequency response of the coupling filter and the mutual coherence of oscillations when the coupling parameters change were considered. Results. The system of couplings between chaotic maps behaves like a wave filter with selective properties, allowing spatial modes with certain wavelengths to exist and suppressing others. The selection of spatial modes is based on the wave characteristic of the coupling filter, the type of which is determined by the radius and the magnitude of couplings. At strong coupling the wave characteristics for ensembles with local and non-local couplings are qualitatively different, therefore they demonstrate essencially different behavior. Discussion. Using spectral methods for dynamics analysis systems with complex network topologies seems to be a promising approach, especially for research of synchronization and multistability in ensembles of chaotic oscillators and maps. The found regularities generalize the results known for ensembles of maps with local couplings. They also can be applied to ensembles of self-sustained oscillators.

Introduction. The paper submits the analysis of existing design solutions of flow dividers used to synchronize hydraulic drives of working bodies of technological and mobile machines. The market demands for multithreaded throttle flow dividers without valves with the controlled division ratio, such as multi-axle vehicle chassis, are identified. The objective of the work was to analyze the possibility and rationale for developing a throttle four-way flow divider without valves with sensing elements of the Venturi tube type. The solution should provide the synchronicity of movement (rotation) of more than three working bodies of technological and mobile machines.Materials and Methods. A patent search for the designs of hydraulic flow dividers is carried out, and systems that require the division of the hydraulic fluid flow into more than two executive bodies are considered. An upgrade option, which allows dividing the flow into four branches, is proposed for the design of a three-channel throttle flow divider without valves.Results. The urgency of developing a multithreaded throttle flow divider without valves for application in industrial and mobile machines is validated. Two types of four-flow dividers are considered, their weaknesses are indicated. It is noted that the development of a multithreaded throttle flow divider based on the designs created in 1989 and 1991 will reduce the number of hydraulic pumps and get rid of the series connection of double-flow dividers. In this way, it is possible to reduce pressure losses in the hydraulic system and implement adaptive control of hydraulic motors of multi-motor mobile machines. The possibility to obtain a divider/combiner into four flows by adding an outlet chamber connected to the membrane chamber through a channel entering the Venturi nozzle on the basis of a three-flow throttle divider is shown. The principle of operation of such equipment is described.Discussion and Conclusions. The principles of construction of throttle flow dividers without valves are considered. An upgrade option is proposed to increase the number of division channels from three to four. However, to validate the operability of this design, a numerical analysis of the various modes of operation of the divider is required — calculation of the reduced volumetric stiffness of its working cavities. The information obtained can be used to modernize the hydraulic units of technological and mobile machines, increase their reliability, manufacturability, and efficiency. The issues that need to be solved in further research are identified.

Topic. The paper is devoted to the study of synchronization of a gyrotron by an external harmonic signal. A theoretical study of gyrotron synchronization processes by means of a computational experiment based on certain traditional models of microwave electronics does not provide a complete description of the synchronization pattern. Therefore, the goal of the paper is to develop a modified quasi-linear model based on an approximation of the electron susceptibility by rational functions. Methods. The developed model allows for bifurcation analysis of synchronization processes. On its basis, stationary states are determined and their stability analysis is carried out. The results are in good agreement with numerical simulation based on the non-stationary theory of a gyrotron with a fixed Gaussian high-frequency field structure. Results and discussion. Resonance curves and synchronization bounds are built on the plane of parameters “amplitude – frequency of external signal”. The case where the gyrotron is in the hard excitation mode is considered, since the maximum efficiency is usually achieved in the hard excitation mode. In general, the results are in qualitative agreement with the picture described earlier for a simpler quasi-linear model of a oscillator with hard excitation, in the case of a sufficiently strong phase nonlinearity.

The article provides a comparative analysis of the structures of synchronization of the motion of electric drives of medium and high power. A comparison of synchronization structures is made in terms of the impact on the final operation of the system and hardware synchronization methods in terms of applicability and maximum performance. The mathematical apparatus is based on the principle of separation of the movements of each of the electric drives and the representation of its transfer function in matrix form. The control ranges and speed of different types of systems are compared experimentally by evaluating the speed of data transmission and evaluating the speed ripple at low revs.

This is the second part of the two-part article, which summarizes the state-of-the-art results in the development of synchronized oscillators based on IMPATT (IMPact ionization Avalanche Transit-Time) diodes. The first part of the paper presented the electrodynamic design of oscillators, which contain a resonant oscillatory system with silicon IMPATT diodes and are synchronized by an external source of microwave oscillations. The second part of the paper considers the methods for stabilizing the parameters of IMPATT oscillators, which make it possible to create coherent power sources in the millimeter wavelength range. The specifics of pulse generators lies in the change in frequency within the microwave pulse relative to the change in temperature, which leads to a change in the impedance of the diode and thus to a phase change with respect to the synchronizing signal. Phase modulation is reduced or completely eliminated (which is necessary to ensure the coherence of the microwave transmitter) by using current compensation, i.e., by using the control current pulse with a special shape. The study demonstrates the expediency of introducing additional heating of the semiconductor structure of the IMPATT diode, which allows the initial temperature of the IMPATT diode in the region of the leading edge of each pulse to remain virtually constant and independent of the ambient temperature. Using these methods on silicon double-drift IMPATT diodes allowed creating synchronized oscillators with high frequency stability and an output power level from 20 to 150 W, which have a high degree of coherence in the synchronization mode with an external signal. The paper also presents the designs and parameters of coherent microwave power sources in the short-wave part of the millimeter wavelength range using the nonlinear properties of the IMPATT diodes in the radio-pulse conversion mode. This mode makes it possible to provide the output power level of the signal at the n-th harmonic Pout ≈1/n, which significantly exceeds the achieved characteristics of the frequency multipliers with charge accumulation, where Pout ≈ 1/n2. The output power of such devices is achieved at the level of 50–20 mW in the 75–180 GHz frequency range with a frequency multiplication factor of 1–15.

The purpose of this work is to research the phenomena of the self-oscillation and the synchronization for the model of business and financial oscillator, which presented as the system of automatic control. Methods. The research methods are the qualitative and numerical methods of the theory of nonlinear dynamical systems and the theory of the bifurcations. Results. This work presents the model of business and financial oscillators as the phase-controlled oscillator and as the frequency-controlled oscillator. The phenomena of the self-oscillation of regular and chaotic oscillations in this model and the synchronization of such oscillations are considered.

Advances in the development of ultrahigh-frequency semiconductor electronics open wide opportunities for developing optimal schemes and designs of microwave power sources in the millimeter wavelength range providing high stability of the frequency and electromagnetic oscillation phase. Synchronized diode generators used in transmit/receive module for active phased array antennas, coherent low-power radar stations, etc. show great promise. The mode of external synchronization of semiconductor generators allows effectively implementing the task of creating output stages of the transmitters with high gain factor, low frequency noise and an output power level corresponding to the maximum power mode. This article presents the first of two parts of the study, which summarizes the results achieved so far in the development of synchronized oscillators based on impact ionization avalanche transit-time (IMPATT) diodes. The first part presents the electrodynamic designs of the oscillators, which are synchronized with an external source of microwave oscillations and contain a resonant oscillating system with a silicon IMPATT diode. The silicon two-drift IMPATT diode was chosen as an active element due to the fact that its use allows reaching significant levels of pulsed microwave power – an order of magnitude higher than those of the most well-known HEMT and pHEMT transistors in the millimeter wavelength range. It is shown that to reduce losses, the oscillating system should be made in the form of a radial resonator with a diode casing, which has distributed parameters. This eliminates the use of additional reactive inhomogeneities in the initial cross-section of the waveguide section of the generator. Due to the low quality factor of the resonant casing of the diode, the generalized quality factor of the microwave circuit takes the minimum value required to implement a stable generator synchronization process in the millimeter wavelength range. The second part of the work will be devoted to synchronized pulse generators with an output power of 20–150 W.

This paper is devoted to construction of reference walking trajectories for developing pedestrian navigation algorithms for smartphones. Such trajectories can be used both for verification of classical algorithms of navigation or for application of machine learning technics. Reconstruction of closed trajectories based on data from foot-mounted inertial measurement units (IMU) is investigated. The advantages of the approach are the use of inexpensive sensors and the simplicity of the presented method. We propose algorithms for reconstruction of smooth 2D pedestrian trajectories based on measurements from a single IMU as well as on combined measurements from two IMU’s. Introduced algorithms are based on application of modified Kalman filter with an assumption of IMU having zero velocity when foot contacts the ground. In case of two measurement units, it is additionally assumed that the positions of the sensors cannot differ significantly from each other. The algorithms were tested on trajectories lasting from 1 to 10 minutes, passing indoors on horizontal surfaces. Obtained results were compared with high precision trajectories acquired with GNSS RTK receivers. Additionally, the process of inter-device time synchronization is investigated and detailed description of the experiments and used equipment is given. The dataset used for verification of proposed algorithms is freely available at: http://gartseev.ru/projects/rtj2021.

Topic and aim. Synchronization in populations of coupled oscillators can be characterized with order parameters that describe collective order in ensembles. A dependence of the order parameter on the coupling constants is well-known for coupled periodic oscillators. The goal of the study is to extend this analysis to ensembles of oscillators with chaotic phases, moreover with phases possessing hyperbolic chaos. Models and methods. Two models are studied in the paper. One is an abstract discrete-time map, composed with a hyperbolic Bernoulli transformation and with Kuramoto dynamics. Another model is a system of coupled continuous-time chaotic oscillators, where each individual oscillator has a hyperbolic attractor of Smale–Williams type. Results. The discrete-time model is studied with the Ott–Antonsen ansatz, which is shown to be invariant under the application of the Bernoulli map. The analysis of the resulting map for the order parameter shows, that the asynchronouis state is always stable, but the synchronous one becomes stable above a certain coupling strength. Numerical analysis of the continuous-time model reveals a complex sequence of transitions from an asynchronous state to a completely synchronous hyperbolic chaos, with intermediate stages that include regimes with periodic in time mean field, as well as with weakly and strongly irregular mean field variations. Discussion. Results demonstrate that synchronization of systems with hyperbolic chaos of phases is possible, although a rather strong coupling is required. The approach can be applied to other systems of interacting units with hyperbolic chaotic dynamics.

The purpose of this study is to describe the complete picture of synchronization of two coupled generators of quasi-periodic oscillations, to classify various types of synchronization, to study features of occurrence and destruction of multi-frequency quasi-periodic oscillations. Methods. The object of the research is systems of ordinary differential equations of various dimensions. The work uses the fourth-order Runge–Kutta method to solve a system of differential equations. Main analysis of the dynamics is carried out on the basis of calculated spectrum of Lyapunov exponents depending on parameters of systems, so-called charts of Lyapunov exponents. Bifurcation trees, winding numbers, phase portraits and Poincare maps were also visualized. ´ Results. Study of the dynamics of two coupled quasi-periodic generators for two sets of operating parameters of the subsystems is carried out. Two cases were studied when a two-frequency torus or chaotic oscillations (destroyed torus) are observed in the first oscillator. The dynamics of the second oscillator demonstrates different types of dynamics with a variation of the frequency detuning: periodic, quasi-periodic and chaotic. It is shown that for all parameters, phase synchronization of generators, broadband synchronization, and the phenomenon of oscillator death are observed. Dynamical regimes picture of the parameter plane frequency detuning – the coupling strength has a universal structure. Exit from the broadband synchronization region with a decrease in the coupling strength is accompanied by a quasiperiodic Hopf bifurcation and the birth of a three-frequency torus. Conclusion. The interaction of the simplest generators of quasi-periodic oscillations gives a rich picture of dynamic regimes: multi-frequency quasi-periodic oscillations with a different numbers of frequencies, chaotic behavior characterized by a different spectrum of Lyapunov exponents. Despite the variety of dynamic regimes, the synchronization picture of two dissipatively coupled quasi-periodic generators has a universal structure. Quasi-periodic phase and broadband synchronization are observed. The destruction of a torus in a subsystem leads to the destruction of multi-frequency tori in the system of two coupled oscillators, as well as a decrease in the variety of types of chaotic attractors.

Purpose of the work is to study spatio-temporal dynamics of limited two-age structured populations that populate a 2D habitat and capable of long-range displacement of individuals. We proposed the model that is the network of nonlocally coupled nonlinear maps with nonlinear coupling function. Conditions for the emergence of different types of heterogeneous spatial distribution, combining coherent and incoherent regimes in different sites and solitary states are studied. Methods. In order to study the multistability of the dynamics in space and time, we used the synchronization factor and the order parameter. In addition, the method for estimating a number of solitary states is proposed. During numerical experiments, we generated many random initial conditions and computed these indicators for asymptotic space-time regime, and estimated the probability of a specific scenario. Results. Three typical regimes of spatio-temporal dynamics are described. The first one is a homogeneous distribution with full or partial synchronization. The probability of this scenario decreases as the strength and/or radius of coupling decreases. The second is a heterogeneous distribution with spots, stripes or labyrinths patterns, corresponding to cluster synchronization. The last one is highly fragmented spots, but in general with coherent dynamics. It was shown that these regimes coexist under certain conditions. Moreover, in most cases, the spatio-temporal dynamics contains randomly located single elements with outbreak of population size (solitary states) regardless of the observed regime of most others. Conclusion. The following paradoxical situation was revealed. As the elements become less coupled and the dynamics more incoherent, the number of solitary states increases. As a result, the elements with outbreak are more often synchronized with each other and form clusters of solitary states mixed with clusters of synchronous populations, or with highly fragmented clusters, or such clusters appear against the background of absolutely non-synchronous dynamics.

Background and Objectives: Methods of population dynamics give the possibility to analyze many biological phenomena by constructing simple qualitative models, which allow to understand their nature and to predict their behavior. This approach is used to study the spread of epidemics of infectious diseases in biological and human populations. The work considers a modified SIRS model of epidemic spread in the form of a lattice of stochastic cellular automata. The model uses dynamic population control with a limitation of the maximum number of individuals in the population and the influence of the disease on reproduction processes. The effect of migration is explored. Materials and Methods: Numerical simulation of the square lattice of cellular automata by means of the Monte Carlo method, investigation of synchronization of oscillations by time-series analisys and by the coherence function. Results: The considered SIRS model demonstrates irregular oscillations in the number of infected individuals at certain values of the parameters. Weak diffusion produces a significant effect on the oscillations, changing their intensity, average period and constant components. The diffusion also leads to synchronization of processes on different regions of the population. Conclusion: The behavior of the lattice cellular automata SIRS model essentially differs from that of the ordinary differential equations. In particular, it can demonstrate the oscillatory regime, which is absent in the mean field approach, as well as the phenomenon of synchronization.

The purpose of this work is to study the dynamics of a weakly inhomogeneous ensemble of three FitzHugh–Nagumo neurons with excitatory synaptic couplings. To single out main types of canard solutions of the system and obtain the regions in parameter space the solutions exist in. Methods. In this paper the dynamics of autonomous systems are studied by using methods based on geometric singular perturbation theory. To study the dynamics of non-autonomous systems we develop an approximate approach and use numerical methods such as obtaining of Poincare maps. Results. The dynamics of the second neuron was studied analytically provided that the first neuron is at rest. The existence of solutions corresponding to different types of periodic oscillations, including canard ones, was shown. To study non-autonomous system, describing the dynamics of third neuron, the approach based on construction of auxiliary autonomous system was developed. It was shown that in the system there exist different types of invariant torus, including canard ones, corresponding to the regimes of various subthreshold and spiking quasi-periodic oscillations of the third neuron. Torus-canards were discovered corresponding to various types of subthreshold-spiking oscillations. Conclusion. The dynamics of a weakly inhomogeneous ensemble of three FitzHugh–Nagumo neurons, the depolarization levels of which linearly increase with their index, and connected in series through chemical synapses, is considered. It was shown that the existence of torus-canards with simple and complex shape is possible in the ensemble. The torus-canards with simple shape correspond either to subthreshold or to spiking oscillations of the ensemble neurons. On the other hand, the torus-canards with complex shape correspond to the regimes of complex subthreshold-spiking oscillations.

Purpose. Study of synchronization of oscillations in ensembles of probabilistic cellular automata that simulate the spread of infections in biological populations. Method. Numerical simulation of the square lattice of cellular automata by means of the Monte Carlo method, investigation of synchronization of oscillations by time-series analisys and by the coherence function. Results. The effect has been found of synchronization of irregular oscillations, similar to the phenomenon of synchronization of chaos in dynamical systems. It is shown that the coupled lattices of cellular automata can demonstrate the effect of phase locking, as well as the tuning of the main frequencies in the oscillation spectra; at strong coupling they also can demonstrate an almost complete synchronization regime. Discussion. The most interesting result of the work is the revealed similarity of the phenomenon of chaos synchronization, which is well known for deterministic systems, with synchronization of irregular oscillations in interacting stochastic ensembles, whose behavior is determined exclusively by probabilistic laws. At the same time, the interaction algorithm, which has been used in the modeling is too idealized, becouse it does not consider the finite speed of diffusion processes. Taking the last into account will probably lead to more complex types of synchronization that has been found in the research.

Background and Objectives: Dynamical systems containing memristive elements, i.e. elements with “memory”, represent a special class of dynamical systems that can be named memristive systems. In memristive systems, the synchronization of oscillations has some features. However, a complete description of these features is still lacking. For the most part, this concerns the synchronization of memristive self-oscillators, both identical and with frequency detuning. In this paper, we study two resistively coupled self-oscillators containing memristive conductivities. We consider both the complete synchronization of identical selfoscillators and the frequency synchronization of self-oscillators with detuning. The features of synchronization effects associated with the memristive nature of partial systems are revealed. The influence of “non-ideality” of memristive elements and the duration of the establishment processes in this case are analyzed. Materials and Methods: Using numerical integration methods for various parameter values, approximate solutions of a system of ordinary differential equations that describe the dynamics of two coupled memristive self-oscillators are obtained. Projections of phase trajectories are plotted on various planes, as well as regions of synchronization of oscillations of the system under study. Results: It is shown that the memristive systems under consideration demonstrate both the effect of complete synchronization (with full identity of partial systems) and the effect of frequency synchronization (in the presence of frequency detuning). The complete synchronization of oscillations is characterized by the presence of a threshold for the coupling, the value of which continuously depends on the initial conditions, in particular, on the initial values of variables that specify the states of memristive elements. With a constant value of the coupling coefficient, there is a continuous dependence of the boundaries of the frequency synchronization region on the initial conditions. The introduction of a parameter characterizing the rate of memristors “forgetting” their initial state (“non-ideality”) leads to the disappearance of the dependence of the type of the steady state on the initial conditions. Conclusion: The fundamental phenomenon of synchronization is inherent in memristive self-oscillators, which allows them to be attributed to the class of self-oscillating systems. The influence of the initial conditions on the effects of synchronization can be considered as a general property of “ideal” memristive systems.

Subject and Purpose. The paper presents a technology of constructing a promising meteor-burst communication system (MBCS) with code division multiplexing. It increases the bandwidth and improves the noise immunity and covert operation of the system. Methods and Methodology. The proposed technology is based on software-defined radio (SDR) and provides MBCS adaptation to the environment conditions by means of software parameter control of the signals and their transfer protocols. It includes a technique of forming a large ensemble of signals with a direct sequence spread spectrum and improved auto- and cross-correlation properties, involves the optimal reception and matched digital filtering of large-base signals. In order to improve the noise immunity, the narrow-band interference rejection in the signal spectrum is proposed and is jointly software installed with the matched filtering. The detection and synchronization techniques effectively working in the non-Gaussian and non-stationary interference conditions gained consideration. Results. A method of forming a large ensemble of direct sequence spread spectrum signals with improved auto- and cross-correlation properties has been software implemented using a pseudorandom permutation of codeword elements of a maximum-length register code. Designed with the use of fast Fourier transforms, algorithms of digital matched filtering and interference rejection as applied to large-base signals have been implemented via field-programmable gate arrays (FPGA). A method of detection and synchronization of large-base signals has been proposed and software implemented on the FPGA basis. Conclusion. The proposed algorithms and their implementation methods make it possible to increase the bandwidth, improve noise immunity and enhance covert operation of the meteor-burst communication system with code division multiplexing.

The main purpose of this paper is to investigate the dynamics of the power grid model with hub cluster topology based on the Kuramoto equations with inertia. It is essential to study the stability of synchronous grid operation mode and to find conditions of its global stability. The conditions that ensure establishment of the synchronous mode instead of coexisting asynchronous ones are considered. Methods. In this paper we use numerical modelling of different grid operation modes. Also we use an approach based on the second Lyapunov method, which allows to give an estimate of the area of safe perturbations that do not violate the synchronous mode. Results. Various power grid operation modes and boundaries of their existence in the parameter space are considered. An approach allowing to estimate the magnitude of safe disturbances that do not violate the synchronous mode, is described. Conclusion. The paper considers a power grid model with hub cluster topology. For hub-clusters of three and four elements, their parameter spaces are partitioned into areas corresponding to different operation modes. In particular, parameter areas with global asymptotic stability of synchronous modes that is with trouble-free operations under any initial conditions has been identified. To characterize the modes of hub clusters outside the areas of global asymptotic stability, estimates of the areas of safe perturbations that do not violate the synchronous grid operation mode is given. Acknowledgements. The work on the study of the dynamic regimes of hub clusters of three and four elements (Section 4) was performed as part of the state assignment of the IAP RAS, project No. 0035–2019–0011. The approach for estimating the magnitude of safe disturbances (Section 5) was developed with support from Russian Foundation for Basic Research (grants No. 18-29-10040, No. 18-02-00406).

Aim. To study the characteristics of carpal tapping in the normal condition and the effect of subclinical anxiety on its parameters with post-stroke epilepsy in adults.Material and methods. We examined 140 people aged from 22 to 55 years. The total sample was divided into 3 observation groups: the first (I) group included healthy volunteers; the second (II) group included the patients with post-stroke frontal lobe epilepsy; the third (III) group included the patients with post-stroke temporal lobe epilepsy. Each group was divided into two subgroups: subgroup Ia (33 people) included healthy volunteers who did not show reliably expressed symptoms of anxiety; subgroup Ib (27 people) included healthy volunteers with subclinical anxiety; subgroup IIa (20 people) included patients with post-stroke frontal lobe epilepsy who did not show reliably expressed symptoms of anxiety; subgroup IIb (20 people) included patients with post-stroke frontal lobe epilepsy with subclinical anxiety; subgroup IIIa (19 people) included patients with post-stroke temporal lobe epilepsy who did not show reliably expressed symptoms of anxiety; subgroup IIIb (21 people) included patients with post-stroke temporal lobe epilepsy with subclinical anxiety. The parameters of carpal tapping were investigated using the modified author’s program “Method of influencing an individual human rhythm through exogenous rhythmic stimulation”.Results. An acceleration of the individual rhythm was found in the presence of subclinically expressed anxiety both in healthy volunteers (from 1.13 Hz to 1.53 Hz) and in patients with post-stroke frontal lobe and temporal lobe epilepsy (from 2.07 Hz to 3, 45 Hz and from 1.83 Hz to 2.82 Hz, respectively). The rate of acceleration of the individual rhythm in patients with post-stroke frontal lobe and temporal lobe epilepsies was higher than in healthy volunteers (1.66 and 1.54 versus 1.35, respectively).Conclusion. The effect of anxiety on the parameters of carpal tapping was greater in patients with post-stroke epilepsy compared with healthy volunteers.

Synchronization of the collective movement of vehicles in the composition of flows in special sections of motor vehicles is one of the most pressing problems in the context of increasing intensity of motor traffic. The aim of the study is to increase the levels of safety of transport and technological processes on sections of serpentine (studs) of the road network by synchronizing the collective movement of vehicles in traffic. According to the stated goal the following tasks are defined: to develop a topological form of auxiliary curves of the highway route on the sections of serpentines of the 1st and 2nd kind; determine the topological dimensions of the minimum permissible distance of the contour of the obverse side of the shrubbery gas-dust-protective forest belt to the axis of the carriageway on the serpentine sections. The researches were carried out on the basis of methods of analytical geometry on a plane and taking into account the topological features of algebraic functions, which described the trajectories of the gradients of the movement of flows of "wide moving clusters" of vehicles. It was established a priori that, according to the theory of the three phases of motor traffic, proposed by B. Kerner, the desynchronization of the collective movement of vehicles in the composition of traffic flows at sections with special traffic conditions leads to a violation of the coherence of these flows. The synchronized traffic flow is transformed into a “wide moving vehicle cluster”. Such desynchronization not only breaks the stability of the modes of transport and technological process, but also causes a decrease in the levels of traffic safety and intensification of the emission of aerosols of gas-dust emissions produced by the flows of vehicles. According to the results of researches, topological parameters and a two-dimensional graphical model of a possible variant of transport and technological optimization of the road network in "studs" of serpentines were developed. The design distance of the contour of the obverse side of the wood-bush gas-dust lane to the axis of the carriageway is determined depending on the angle of turn of the highway. Accordingly, the proposed optimization of the design parameters of the road network in the "studs" of serpentines provides for the possibility of synchronization of collective traffic of vehicles in the composition of traffic flows, which provides stabilization of the implementation of transport and technological operations and, as a consequence, increases the overall level of safety of the motor complex. Further research should be aimed at ensuring the safe transport and technological modes of operation of the motor transport complex in the conditions of growth of the share of autonomous robotic unmanned vehicles in the composition of motor transport flows.

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The purpose of this study was to evaluate the impact of the use of slow release urea products from the cooking result of gebang starch (putak) with urea in concentrate feed as feed supplements on the growth of Bali cattle. Sixteen male Bali cows (body weight of 192.71±19.17 kg) used in a completely randomized design 4 x 4. Livestock were randomly allocated to get one of the treatments of the use of purea (cooking of putak meal with 6% urea) in concentrate feed, namely T0: putak meal mixed with urea (the amount of putak meal 60% in concentrate, the amount of urea 3% from putak meal), T1: purea 20%, T2: purea 40%, T3: purea 60%. King grass is used as basal feed in comparison with a 60: 40 concentrate. The research results showed the consumption of dry matter, organic matter, crude protein, crude fiber and total digestible nutrients did not differ due to the use of purea, but the digestibility of dry matter, organic matter, crude protein and crude fiber, weight gain, and efficiency of feed use differ among the treatments. The use of purea to 40% level in concentrate feed is better in increasing the growth compared to the use of urea mixture with putak meal without cooking. The use of purea does not cause cattle to experience health problems or poisoning.

The results presented research OFDM system synchronization by using one of the basic properties of the continuous Fourier transform, characterized by the duality between a convolution in the time domain, and multiplying the frequency domain, which is not fully extended to the discrete case. For its correct application to the digital system design OFDM linear convolution sampling replaced the circular convolution. This approach reduces the computational analysis synchronization of its complexity and requires the formation of training sequences or pilot data. The result is a matrix that takes into account the deviation of the analyzed samples in the form of random Gaussian processes with zero mean value, allowing to estimate the amplitude of the subcarriers for an arbitrary level of dispersion of random processes.

The application of synchronized artificial neural networks for generation of a common cryptographic key and an attack by deferred search on these networks with the purpose of obtaining this key are considered.

It was established that the rosynchronization of the collective movement of vehicles as part of traffic flows in areas with special traffic conditions leads to a violation of the coherence of these flows, which leads not only to a decrease in the safety levels of the transport process, but also to the intensification of aerosol emissions of gas-dust emissions traffic flows. According to the results of studies that were carried out on the basis of analytical geometry methods on the plane and taking into account the topological features of algebraic functions, which describe the trajectories of the gradients of the traffic flow of vehicles, topological parameters and two-dimensional graphical models of possible options for transport and technological optimization of the road network were developed. The dimensions of the minimum allowable width of the carriageway in the nodes of the road network for motor traffic flows are determined depending on the intensity of traffic on roads of various categories. Accordingly, the proposed optimization of the design parameters of the road network at the intersection of motor traffic flows provides for the possibility of synchronizing the collective movement of motor vehicles as part of traffic flows, which stabilizes the performance of transport and technological operations and, consequently, increases the overall safety level of the motor complex.

The article presents a generalized computer model of electric drive with pulse-phase control of angular velocity. The model is created on the basis of the pulsed frequency-phase discriminator model with additional functionality that allows to investigate the most effective, from the point of view of improvement of dynamic indicators of quality of regulation, ways of management of the given electric drive. This significantly reduces the simulation time, which accelerates the study of synchronous-common-mode electric drive and phase-locked electric drive in the high speed areas.

Copyright of System Research & Information Technologies / Sistemnì Doslìdžennâ ta Ìnformacìjnì Tehnologìï is the property of Institute for the Applied System Analysis at the NTUU KPI and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Relevance of the study. To improve the quality of service (QoS), the work of all network technologies, protocols, and individual traffic management mechanisms is constantly optimized. It is known that the quality of information transmission in modern telecommunication equipment is affected by the quality of synchronization devices. Synchronization is a means of maintaining the operation of all digital equipment in a data transmission network at one average speed, which must exist at three levels: bit synchronization, synchronization at the level of channel intervals (time slot) and frame synchronization. Therefore, the lack of synchronization of the computer system at the required level can lead to a significant decrease in QoS. At the same time, the requirements for ensuring these indicators are significantly tightened in the face of an increase in the load of network resources. Subject of study: computer system synchronization. The aim of the article is to develop a method for diagnosing synchronization disturbances in the telecommunications network of a computer system of critical application by increasing the resolution of an acousto-optical spectrum analyzer. Research results. The influence of non-stationary data transmission in the telecommunications subsystem of the computer system under study is analyzed. The analysis and classification of the causes of computer network synchronization failure of a critical application computer system is carried out. The article describes the consequences of a violation of computer network stabilization for ensuring the quality of service provided by various frequently used services. Proposed the use of acousto-optic spectrum analyzer with spatial integration for diagnostics of violations of the synchronization network. In work the analysis of the use of acousto-optic spectrum analyzers. The conducted research allowed us to obtain an analytical expression for the output signal of the spectroanalyzer when two rectangular pulses with different carrier frequencies, durations and delay times are received at its input. This result, as well as the numerical calculations provided, allowed us to develop General recommendations for increasing the resolution of the acousto-optical spectrum analyzer, and thus create theoretical prerequisites for improving the synchronization of the computer system. The given analytical relations and numerical estimates were experimentally verified by means of system simulation. Conclusions. As a result of the research, a method of diagnostics of synchronization violations in the telecommunications network of a computer system of critical application was proposed. The method is based on increasing the resolution of the measuring system based on an acoustooptic spectrum analyzer.

The results of the theoretical and experimental research of the original synchronized dualchambered hydromechanical system with indirect regulated valve systems of different structural configuration are shown.

Generalized structural and conceptual hydrokinetic analytical models, and technique for developing a mathematical model of multiengined hydromechanical systems are presented.

The subject of the present paper is an exemplary model for the processing of the mass archaeological material – the pottery. For this aim, a typological system has been developed and it consists of Whole Vessels Typology (WVT) and Pottery Fragment Typology (PFT). During the pottery processing by the two typologies, an attempt for relating the whole vessels’ data with the fragmentary material was made. This gives the opportunity to make a connection between certain pottery details – like different types of rims, decoration, handles and bottoms – with certain types of the respective categories of vessels. In addition, separate types and subtypes of the PFT are very well dated in a number of settlements and separate layers in them which let us relate the fragmentary material with WVT and gives a chance for a precise dating not only of certain types and subtypes, but entire typological lines. This way the pottery becomes а reliable dating material for the medieval settlements of the Byzantine cultural circle.

Copyright of System Research & Information Technologies / Sistemnì Doslìdžennâ ta Ìnformacìjnì Tehnologìï is the property of Institute for the Applied System Analysis at the NTUU KPI and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The article proposes a method of joint analysis of multidimensional financial time series based on the evaluation of the set of properties of stock quotes in a sliding time window and the subsequent averaging of property values for all analyzed companies. The main purpose of the analysis is to construct measures of joint behavior of time series reacting to the occurrence of a synchronous or coherent component. The coherence of the behavior of the characteristics of a complex system is an important feature that makes it possible to evaluate the approach of the system to sharp changes in its state. The basis for the search for precursors of sharp changes is the general idea of increasing the correlation of random fluctuations of the system parameters as it approaches the critical state. The increments in time series of stock values have a pronounced chaotic character and have a large amplitude of individual noises, against which a weak common signal can be detected only on the basis of its correlation in different scalar components of a multidimensional time series. It is known that classical methods of analysis based on the use of correlations between neighboring samples are ineffective in the processing of financial time series, since from the point of view of the correlation theory of random processes, increments in the value of shares formally have all the attributes of white noise (in particular, the "flat spectrum" and "delta-shaped" autocorrelation function). In connection with this, it is proposed to go from analyzing the initial signals to examining the sequences of their nonlinear properties calculated in time fragments of small length. As such properties, the entropy of the wavelet coefficients is used in the decomposition into the Daubechies basis, the multifractal parameters and the autoregressive measure of signal nonstationarity. Measures of synchronous behavior of time series properties in a sliding time window are constructed using the principal component method, moduli values of all pairwise correlation coefficients, and a multiple spectral coherence measure that is a generalization of the quadratic coherence spectrum between two signals. The shares of 16 large Russian companies from the beginning of 2010 to the end of 2016 were studied. Using the proposed method, two synchronization time intervals of the Russian stock market were identified: from mid-December 2013 to mid- March 2014 and from mid-October 2014 to mid-January 2016.

The research states that phase synchronization of fluctuations indicates the areas of phase co-ordination, while the indicator of fluctuation homogeneity characterizes the difference of fluctuation amplitudes at a given time. From a practical point, it is important not only the presence of matches for common fluctuations (measured through homogeneity or synchronization), but the revealing of overwhelming number of matches is also essential, as it enables to identify the lagged trends in development. The paper discusses the approaches to evaluate homogeneity of fluctuations between the basic economic system and a comparative one on the basis of the similarity analysis of impulse-reaction and indicators of mutual correlation. It is indicated that the consistency in the dynamics of two economic variables could be investigated through the correlation of frequency matches, while the phase changes could be detected through leading / guided elements. In order to assess the similarity of business cycles between different national economies the trend deviation values of environmental and economic performance can be used. It is stated that the value of similarity of ecological and economic fluctuations of related economic systems (based on the normalized performance indicators) may be less than unity, because fluctuations can be synchronized imperfectly and / or have different amplitude. The paper analyzes the fluctuation calculation and evaluates cyclic synchronization components of NO2 and SO2 emissions for Germany and Poland.

In this paper, the self-consistent model was considered, consisting of a system of oscillators, the coupling between them was assumed to be integral (due to the fields formed as a result of their co-radiation). With the help of this model, the features of synchronization by waves of finite amplitude of a system of oscillators were refined, the initial phase values of which are random. The effect of nonlinearity, in particular, due to the change in the mass of the oscillator due to relativistic effects, was taken into account. It was shown that the nonlinearity does not violate the nature of the energy exchange between the wave and the oscillator system, leading only to a slight decrease in the efficiency of such an exchange.

The aim of the present study was to investigate the features of interaction of low-frequency rhythms in delta band of electroencephalogram (EEG) and processes in vegetative regulation of circulation with respiration. Materials and methods. 19 leads of EEG, photoplethysmogram (PPG) and respiration were simultaneously recorded in four healthy males (19-25 years old) during 30 minutes physiological test with linearly increasing frequency of respiration. Modern methods of nonlinear dynamics were used to diagnose the presence of phase and frequency synchronization between respiration and low-frequency rhythms in delta band of EEG and in PPG. Results. We found significantly long sections of synchronization of delta rhythms in cervical leads of EEG and low-frequency rhythms in PPG by respiration with linearly increasing frequency. Conclusion. Obtained results correlate well with established hypothesis which suggest that low-frequency rhythms in baroreflectory regulation of circulation are in complex dynamic relationships with structures of brain stem. A method was proposed for quantitative evaluation of synchronization strength between respiration and low-frequency rhythms in electrical brain activity in physiological tests with respiration with frequency linearly increasing in time.

Relevance of the study is caused by the need to improve the effectiveness of approaches to synchronization of non-identical interconnected dynamical systems under conditions of considerable uncertainty. The main aim of the study is to design a robust tracking system for the slave systems the reference the trajectory (task) for which is a synchronized output signal of the master system; to evaluate the implementation of specific dynamic and static parameters, such as settling time of the transient component and the allowable synchronization error; to study robust properties at deviation of slave system parameters from the nominal ones by ±50 %. Method of study: the method of Lyapunov function, automatic control theory, the elements of synchronization and chaos theory; simulation on Matlab/Simulink. The main feature of the method is the use of a new type of controls - "robust equivalent control" - to design robust control systems and to interchange interconnected slave systems without compensators of joints cross channels. Robust controller is the PDn-1 controller with adjustable gain. The possibility of infinite gain magnification without loss of stability allows suppressing general components of uncertain models of slave systems to an arbitrarily small value. This ensures a high tracking (timing) accuracy of the reference trajectory for a wide range of uncertainties. Results and conclusions. Numerical modeling of synchronization systems with different internally regular and chaotic oscillators has shown simplicity and high efficiency of the proposed approach. Really, the synchronization error can be reduced to an arbitrarily small value. However, this requires the use of high gain values ??of the regulator. High performance of robust dynamic mode is achieved. This is proved by the high concentration of beams of transient characteristics of slave systems in the vicinity of the nominal trajectory. The author managed to avoid the mathematical difficulties occur when synthesizing robust tracking systems. The disadvantages of the proposed methodology are reinforcement of the high-frequency interferences having immediate access to the controller as well as the use of output derivative to form PDn-1 controller. Moreover, not every object is capable of implementing the high gain.

Objective: To identify criteria for electroencephalogram (EEG) synchronization in patients with post-traumatic stress disorder (PTSD) exhibiting high levels of functional stress and signs of maladaptation., Material and Methods: Two groups of male subjects aged 23-38 years were examined: a group of subjects receiving therapy for PTSD at a medical center; and a group of healthy subjects who regularly practiced psychophysical relaxation sessions. EEG, an innovative method for analyzing brain synchronizing currents, and the Spielberger State-Trait Anxiety Inventory were used., Results: Criteria for the formation of patterns of synchronization of neural networks were found in subjects of the therapy group, who have a high level of psychofunctional stress and signs of maladaptation against the background of PTSD in combination with severe anxiety and impaired cognitive abilities., Conclusion: Alpha wave synchronization analysis can be used to more accurately diagnose the level of psychofunctional stress in individuals at risk of developing psychophysical disorders. The results of the work suggest the use of technologies that increase the ability to synchronize brain biocurrents to develop programs for correcting psychophysical status, such as relaxation exercises.