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Current earthquake forecasting approaches are mainly based on probabilistic assumptions, as earthquakes seem to occur randomly. Such apparent randomness can however be caused by deterministic chaos, rendering deterministic short‐term forecasts possible. Due to the short historical and instrumental record of earthquakes, chaos detection has proven challenging, but more frequently occurring slow slip events (SSE) are promising candidates to probe for determinism. Here, we characterize the SSE signatures obtained from GNSS position time series in the Hikurangi Subduction Zone (New Zealand) to investigate whether the seemingly random SSE occurrence is governed by chaotic determinism. We find evidence for deterministic chaos for stations recording shallow SSEs, suggesting that short‐term deterministic forecasting of SSEs, similar to weather forecasts, might indeed be possible over timescales of a few weeks. We anticipate that our findings could open the door for next‐generation SSE forecasting, adding new tools to existing probabilistic approaches. Plain Language Summary: Since earthquakes appear to occur randomly, the currently available probabilistic predictions are based on past earthquake records. These predictions estimate the likelihood of an earthquake of a given magnitude occurring within a defined time period. In contrast to such probabilistic approaches, deterministic systems are fully predictable, albeit often confined to short time scales due to their potential chaotic behavior. Probing for deterministic predictability in the earthquake cycle is intractable due to the limited historical instrumental record. However, frequently occurring slow slip events ‐ captured by transient GNSS displacements that can last several weeks ‐ provide a unique opportunity to explore deterministic predictability in these types of slow earthquakes. By studying GNSS time series from various stations on New Zealand's North Island, we have discovered evidence suggesting that these irregularly occurring slow slip events might be governed by chaotic determinism. This implies the potential to forecast both timing and magnitude of slow slip events a few weeks in advance using deterministic methods, much like we predict weather patterns. Consequently, our theoretical findings could therefore pave the way for innovative approaches to short‐term slow slip forecasting. Key Points: Nonlinear analysis of GNSS displacement time series unveils evidence for deterministic chaos in slow slip events in New ZealandOur theoretical findings imply that irregularly occurring slow slip events could potentially be forecasted a few weeks in advance [ABSTRACT FROM AUTHOR]

Abstract Current earthquake forecasting approaches are mainly based on probabilistic assumptions, as earthquakes seem to occur randomly. Such apparent randomness can however be caused by deterministic chaos, rendering deterministic short‐term forecasts possible. Due to the short historical and instrumental record of earthquakes, chaos detection has proven challenging, but more frequently occurring slow slip events (SSE) are promising candidates to probe for determinism. Here, we characterize the SSE signatures obtained from GNSS position time series in the Hikurangi Subduction Zone (New Zealand) to investigate whether the seemingly random SSE occurrence is governed by chaotic determinism. We find evidence for deterministic chaos for stations recording shallow SSEs, suggesting that short‐term deterministic forecasting of SSEs, similar to weather forecasts, might indeed be possible over timescales of a few weeks. We anticipate that our findings could open the door for next‐generation SSE forecasting, adding new tools to existing probabilistic approaches.

In this paper, the applied problems of designing a bridge resonant converter with a high-voltage arc ignition system in the channel of an electric arc motor is solved. The development of a bridge resonant power supply is presented, a review and analysis of power sources of arcjet thruster of various capacities is carried out. The theoretical aspects of calculating the main parameters of the source are considered. The transfer function describing the gain of the resonant circuit of the power supply is given. With the help of the transfer function, gain diagrams are constructed for various values of the Q-factor of the contour. A prototype of a power supply, a starting system and an arcjet thruster is presented. A series of experiments aimed at identifying the operability of the source is carried out. According to the experimental results, the maximum output power of the source wiz 182,4 watts, and the maximum efficiency is 87,5 %. Frequency spectra of the output current of the power supply are obtained. The current-voltage characteristics for the Ar and N2 are constructed. In the course of the study, phenomena related to the chaotic dynamics of the arc in the engine channel are discovered. Chaotic fluctuations are observed at the moment of starting the engine and disappeared after steady-state operation.

Purpose of the article is to illustrate the genesis, meaning and significance of the functional Schroder equation, introduced in the theory of iterations of rational functions, for the theory of deterministic chaos by analytical calculations of exact trajectory solutions, invariant densities and Lyapunov exponents of one-dimensional chaotic maps. We demonstrate the method for solving the functional Schroder equation for various chaotic maps by passing to a topologically conjugate mappings, for which finding the exact trajectory solution is a simpler mathematical procedure. Results of the analytical solution of the Schroder equation for 12 chaotic mappings of various types and the calculation of the corresponding expressions for exact trajectory solutions, invariant densities and Lyapunov exponents are presented. Conclusion is made about the methodological expediency of formulating and solving the Schroder equations by the study of the dynamics of one-dimensional chaotic mappings.

The subject of the article is a variant of an efficient algorithm for synthesizing a dual discrete model and controller for tracking a given trajectory of a dynamic nonlinear, nonstationary black box object, using standard procedures for diagonalizing the state matrix, which makes it possible to simplify obtaining control values in numerical form and reduce the number of calculations. The current article presents one the possible solutions to the problem of regulator synthesis to ensure stable development of a given trajectory of motion of a nonlinear, non-stationary object of "black box" type using the concept of dual control. The task was set to simplify the previously proposed synthesis algorithm for the adaptive control of dynamic nonlinear, non-stationary objects using the example of first-order object of the "black box" type, using standard procedures for the diagonalization of the state matrix. An extended state matrix is the basis for obtaining a control model and predicting the behavior of a nonlinear non-stationary object, which in turn makes it possible to effectively use the concept of dual control. Methods used in the work are based on concept of dual control, nonlinear dynamic models, matrix theory, difference equations. Obtained results of this work consist of the development of a version of a dual nonparametric controller of nonstationary nonlinear processes, which has adaptive properties, does not require knowledge of the physics of functioning of the control object, is presented in the form of a simple algebraic formula that does not contain coefficients that require adjustment. Conclusion. Scientific novelty lies in the application of each interval matrix operator control for the diagonalization of the state submatrix. This operator is used for subsequent calculation of the control action. This approach enables the use of a standard diagonalization procedure using mathematical applications. The results are presented in the form of a final formula that does not require use of matrix operations during control, which makes it possible to simplify the synthesis of the controller using standard mathematical procedures.

Modeling of ecological processes is demonstrated using a newly developed nonlinear dynamics model of microbial populations, consisting of a 4-variable system of coupled ordinary differential equations. The system also includes a modified version of the Monod kinetics equation. The model is designed to simulate the temporal behavior of a microbiological system containing a nutrient, two feeding microbes and a microbe predator. Three types of modeling scenarios were numerically simulated to assess the instability caused by (a) variations of the nutrient flux into the system, with fixed initial microbial concentrations and parameters, (b) variations in initial conditions, with fixed other parameters, and (c) variations in selected parameters. A modeling framework, using the high-level statistical computing languages MATLAB and R, was developed to conduct the time series analysis in the time domain and phase space. In the time domain, the Hurst exponent, the information measure–Shannon’s entropy, and the time delay of temporal oscillations of nutrient and microbe concentrations were calculated. In the phase domain, we calculated a set of diagnostic criteria of deterministic chaos: global and local embedding dimensions, correlation dimension, information dimension, and a spectrum of Lyapunov exponents. The time series data are used to plot the phase space attractors to express the dependence between the system’s state parameters, i.e., microbe concentrations, and pseudo-phase space attractors, in which the attractor axes are used to compare the observations from a single time series, which are separated by the time delay. Like classical Lorenz or Rossler systems of equations, which generate a deterministic chaotic behavior for a certain range of input parameters, the developed mathematical model generates a deterministic chaotic behavior for a particular set of input parameters. Even a slight variation of the system’s input data might result in vastly different predictions of the temporal oscillations of the system. As the nutrient influx increases, the system exhibits a sharp transition from a steady state to deterministic chaotic to quasi-periodic and again to steady state behavior. For small changes in initial conditions, resulting attractors are bounded (contrary to that of a random system), i.e., may represent a ‘sustainable state’ (i.e., resilience) of the ecological system.

Simple Summary: Currently, knowledge on chaos has developed rapidly, and the link between cancer and "genomic chaos" seems obvious. Hopes for a deeper understanding of cancer, allowing cancer modeling, therefore relate to the meaning of the term "chaos". It has many meanings, however. Chaos theory and medicine are conceptually quite distant, requiring the comparison and agreement of terms. This article was written by three authors whose fields cover both medical problems and complex dynamic networks suitable for modeling cancer, including chaotic phenomena. The article provides, first of all, a coherent, common interpretative basis linking chaos with modeling tools, which should significantly facilitate teams of specialists from various fields to undertake specific work on simulating cancer-related phenomena. In the search of theoretical models describing cancer, one of promising directions is chaos. It is connected to ideas of "genome chaos" and "life on the edge of chaos", but they profoundly differ in the meaning of the term "chaos". To build any coherent models, notions used by both ideas should be firstly brought closer. The hypothesis "life on the edge of chaos" using deterministic chaos has been radically deepened developed in recent years by the discovery of half-chaos. This new view requires a deeper interpretation within the range of the cell and the organism. It has impacts on understanding "chaos" in the term "genome chaos". This study intends to present such an interpretation on the basis of which such searches will be easier and closer to intuition. We interpret genome chaos as deterministic chaos in a large module of half-chaotic network modeling the cell. We observed such chaotic modules in simulations of evolution controlled by weaker variant of natural selection. We also discuss differences between free and somatic cells in modeling their disturbance using half-chaotic networks. [ABSTRACT FROM AUTHOR]

This paper presents the generalized information system theory, which is enlarged into pure quantum systems using wave probability functions. The novelty of this approach is based on analogies with electrical circuits and quantum physics. Information power was chosen as the relevant parameter, which guarantees the balance of both components—information flow and information content. Next, the principles of quantum resonance between individual information components, which can lead to emergent behavior, are analyzed. For such a system, adding more and more probabilistic information elements can lead to better convergence of the whole to the resulting trajectory due to phase parameters. The paper also offers an original interpretation of information "source–recipient" or "resource–demand" models, including not yet implemented "unused resources" and "unmet demands". Finally, possible applications of these principles are shown in several examples from the quantum gyrator to the hypothetical possibility of explaining some properties of the consciousness. [ABSTRACT FROM AUTHOR]

In the article are presented general principles of modeling vibrations in discrete structures formed in the form of special matrix forms of the Latin square (Sudoku type) are presented. The signs of structural and functional self-similarity for the matrix structures of standard Sudoku grids are formulated. It is shown that the structural principle can be interpreted as the implementation of the second iteration in the scale scaling algorithm characteristic of fractal objects. The signs of functional self-similarity of structures include the property of additive conservation of grid shapes to the requirements of Sudoku, which is formulated as a theorem. It is proved that the matrix sums of Sudoku constants and grids of arbitrary sizes, obtained taking into account the introduced cyclic ranking rule, will satisfy the three required Sudoku requirements. It is determined that by performing a given sequence of group shift operators, it is possible to establish a specific scenario for dynamically changing the state of a structure on a discrete time scale. It has been established that the evolution operators of linear-type group translations lead to matrix transformations of Sudoku grids from the set of equivalent ones (concerning the original ones), and the vortex-type group shifts operators to matrix transformations from many essentially different networks. The modes of harmonic, chaotic, and hybrid vibrations for structures of arbitrary size are considered. The requirements for transformations of the operators of the evolution of structures that provide the implementation of the considered modes are formulated. The results of modeling chaotic oscillatory processes by cycles of states of a discrete system that form similarities of attractor paths are analyzed. The principle of synchronization of chaotic states of matrix structures is established. The possibility of simulating the modes of beatings of oscillations in discrete cellular structures organized in the form of two-level matrix forms is substantiated. Specific examples show the results of simulating beatings of oscillations in cycles of changing states of a discrete system for two types of beats: similar to the result of a superposition of harmonic vibrations at multiple frequencies in the theory of radio signals, as well as noise-like beats.

In the search of theoretical models describing cancer, one of promising directions is chaos. It is connected to ideas of “genome chaos” and “life on the edge of chaos”, but they profoundly differ in the meaning of the term “chaos”. To build any coherent models, notions used by both ideas should be firstly brought closer. The hypothesis “life on the edge of chaos” using deterministic chaos has been radically deepened developed in recent years by the discovery of half-chaos. This new view requires a deeper interpretation within the range of the cell and the organism. It has impacts on understanding “chaos” in the term “genome chaos”. This study intends to present such an interpretation on the basis of which such searches will be easier and closer to intuition. We interpret genome chaos as deterministic chaos in a large module of half-chaotic network modeling the cell. We observed such chaotic modules in simulations of evolution controlled by weaker variant of natural selection. We also discuss differences between free and somatic cells in modeling their disturbance using half-chaotic networks.

Nowadays interest of the deterministic differential system of Lorentz equations is still primarily due to the problem of gas and fluid turbulence. Despite numerous existing systems for calculating turbulent flows, new modifications of already known models are constantly being investigated. In this paper we consider the effect of stochastic additive perturbations on the Lorentz convective turbulence model. To implement this and subsequent interpretation of the results obtained, a numerical simulation of the Lorentz system perturbed by adding a stochastic differential to its right side is carried out using the programming capabilities of the MATLAB programming environment.

This paper presents the generalized information system theory, which is enlarged into pure quantum systems using wave probability functions. The novelty of this approach is based on analogies with electrical circuits and quantum physics. Information power was chosen as the relevant parameter, which guarantees the balance of both components—information flow and information content. Next, the principles of quantum resonance between individual information components, which can lead to emergent behavior, are analyzed. For such a system, adding more and more probabilistic information elements can lead to better convergence of the whole to the resulting trajectory due to phase parameters. The paper also offers an original interpretation of information “source–recipient” or “resource–demand” models, including not yet implemented “unused resources” and “unmet demands”. Finally, possible applications of these principles are shown in several examples from the quantum gyrator to the hypothetical possibility of explaining some properties of the consciousness.

Background: In the present study, we analyzed stimulus-induced emotional changes in fetuses and mothers by using the Lyapunov exponent (hereafter λ1) and attractors. Objective: We also investigated how emotions change in fetuses and mothers over the course of pregnancy. Methodology: We measured heart sounds under five conditions: without external stimulation, while the mother's recorded voice was being heard, after the mother's recorded voice had finished being heard,while a stranger's recorded voice was being heard and after the stranger's recorded voice had finished being heard. We used one-way analysis of variance to analyze differences among the λ1 of fetal and maternal heart sounds under these five conditions. To observe the time-series characteristics of emotional responses, we calculated the moving average of the numbers of significantly different condition pairs. Results: Based on moving average results, we confirmed three emotional phases in fetuses and mothers. Fetal phase I was around 20 weeks of pregnancy, phase II was from around 21 weeks of pregnancy to around 26 weeks, and phase III was from around 27 weeks to before birth. Maternal phase I occurred at around 19 weeks of pregnancy, phase II was around 20 weeks to 26 weeks, and phase III was from around 27 weeks to before delivery. Fetal attractors did not change in response to strangers' vocal stimuli but did change dramatically in response to mothers' vocal stimuli from Phase I to Phase III, from nearly structureless attractors to chaotic attractors. Maternal attractors were consistently chaotic attractors from Phase I to Phase III and exhibited little change over the course of pregnancy. Changes in fetal and maternal attractors under different conditions suggested the occurrence of entrainment. Conclusions: The above results conceivably arise from the self-organization ability of fetuses and mothers. [ABSTRACT FROM AUTHOR]

In this work, we derive Born’s rule from the pilot-wave theory of de Broglie and Bohm. Based on a toy model involving a particle coupled to an environment made of “qubits” (i.e., Bohmian pointers), we show that entanglement together with deterministic chaos leads to a fast relaxation from any statistical distribution ρ(x) of finding a particle at point x to the Born probability law |Ψ(x)|2. Our model is discussed in the context of Boltzmann’s kinetic theory, and we demonstrate a kind of H theorem for the relaxation to the quantum equilibrium regime.

Many real phenomenona preserves the properties of chaotic dynamics. However, unambiguous determination of belonging to a group of chaotic systems is difficult and complex problem. The main purpose of this paper is to present compound method of time series classification which is basically directed to the detection of chaotic behaviors. The method has been designed for differentiation of three types of time series: chaotic, periodic and random. Our approach assumes, that more reliable information about the dynamics of the system will provide the compilation of several methods, than any individual. This paper focuses on choosing a good set of methods and analysis of their results. In our investigation, we used the following methods and indicators: time delay embedding, mutual information, saturation of system invariants, the largest Lyapunov exponent and Hurst exponent. We checked the validity of the methods applying them to three kinds of basic systems which generate chaotic, periodic and random time series. As a summary of this paper, all selected methods and indicators computed for generated times series have been summarized in the table, which gives the authors a possibility to conclude about type of observed behavior.

This research represents a detailed insight into the modern and popular hybridization of deterministic chaotic dynamics and evolutionary computation. It is aimed at the influence of chaotic sequences on the performance of four selected Differential Evolution (DE) variants. The variants of interest were: original DE/Rand/1/ and DE/Best/1/ mutation schemes, simple parameter adaptive jDE, and the recent state of the art version SHADE. Experiments are focused on the extensive investigation of the different randomization schemes for the selection of individuals in DE algorithm driven by the nine different two-dimensional discrete deterministic chaotic systems, as the chaotic pseudorandom number generators. The performances of DE variants and their chaotic/non-chaotic versions are recorded in the one-dimensional settings of 10D and 15 test functions from the CEC 2015 benchmark, further statistically analyzed.

Main results of theoretical and experimental investigations since the 1980s of 20th century that led to the formation and developing of new fundamental science discipline: 'Fractal Radio Physics and Fractal Radio Electronics: Fractal Radio Systems Designing' are briefly classified in the study. [ABSTRACT FROM AUTHOR]

We will show that, unlike usual (i.e., nonimpulsive) differential equations, the standard Sharkovsky cycle coexistence theorem applies easily to impulsive, scalar, ordinary differential equations. In fact, there is a one-to-one correspondence between the subharmonic solutions of given orders and periodic points of the same orders of the associated Poincaré translation operators, provided a uniqueness condition is satisfied. Despite the fact that the usage of the Poincaré operators in the context of impulsive differential equations is neither new, nor original, and that the application of the Sharkovsky celebrated theorem becomes in this way rather trivial, as far as we know, an appropriate theorem has not yet been formulated. As a by-product, the relationship of impulsive differential equations to deterministic chaos will also be clarified. In order to demonstrate the merit of the basic idea, some less trivial extensions for discontinuous and multivalued impulses will still be briefly done, along with indicating the situation in the lack of uniqueness. [ABSTRACT FROM AUTHOR]

In this paper, we consider the online single machine scheduling problem to minimize the maximum weighted completion time of the jobs. For the preemptive problem, we show that the LW (Largest Weight first) rule yields an optimal schedule. For the non-preemptive problem, Li [Li, W (2015). A best possible online algorithm for the parallel-machine scheduling to minimize the maximum weighted completion time. Asia-Pacific Journal of Operational Research, 32(4), 1550030 (10 pages)] presented a lower bound 2, and then provided an online algorithm with a competitive ratio of 3. In this paper, we present two online algorithms with the best-possible competitive ratio of 2 for the non-preemptive problem. [ABSTRACT FROM AUTHOR]

The article presents three models which attempt to predict when individuals will try something new. A decision making situation may be modeled by a choice situation in which an individual has a dichotomous deterministic choice. The stochastic model is looked at, in which individuals are asked for their best estimate of their target level of performance, including the costs and rewards associated with it. The author treats the decision of whether or not to adopt an innovative strategy as a stochastic variable representing the probability of innovation.

Iterated quantum protocols with measurement-based selection lead to deterministic chaos for the evolving pure state representing an ensemble of qubits. Deterministic chaos for the pure quantum state may lead to ergodic evolution in the sense that initial states from any small area on the Bloch sphere will cover the whole sphere after a finite number of iterations. We realize two steps of an ergodic protocol in a photonic experiment, where initial qubit states are encoded in the polarization and path degrees of freedom of down-converted photons stemming from a parametric process. We numerically analyze the effect of noise on the time evolution and show that the protocol, described by a Lattès map, remains quasi-ergodic for any initial state if the initial noise is small. Tomographic reconstruction of the quantum states throughout the evolution is consistent with simulations and thus demonstrates ergodicity of the quantum dynamics.

The aim of the present paper was to study chaotic behavior in a resistor–inductor diode circuit induced by frequency modulation. Time dependences of voltage and current showed an extremely chaotic response of this system. Based on these dependences, the phase space was built. A bifurcation diagram was constructed and based on it, the Feigenbaum constant was calculated and verified with reliable and noticeable accuracy. [ABSTRACT FROM AUTHOR]

Aim - combined use of frequency and nonlinear analysis methods for obtaining hypnograms by analyzing electroencephalographic (EEG) signals during somnological studies. Methods. Frequency filtering methods were used for preliminary treatment of EEG signals before the following nonlinear analysis. As non-linear methods of analysis we used fractal methods of deterministic chaos, such as Hurst’s method of the normalized amplitude, approximate entropy method, calculation of the correlation integral by Grassberger and Procaccia’s method. For the possibility of applying the last two methods we used quasi phase space recovery method according to the Taken’s theorem. As a result of non-linear analysis we obtained hypnograms reflecting the transition between the stages of sleep in patients undergoing somnological examination. To assess the reliability of the results, they were compared to the hypnograms obtained by the classical method based on the rules of Rehchaffen and Keyls. Also the problems associated with the occurrence of various types of interference were considered and methods for reducing their influence on the final results were suggested. Results. We can conclude that using these methods with appropriate selection of the parameters, employing the necessary normalization of raw data, and averaging the results allow us to obtain hypnogram having a full match of defined phases of sleep for about half of the periods recorded by EEG. To obtain these results it is sufficient to use only one channel of EEG recording.

In this paper, evolutionary technique Differential Evolution (DE) is used for the evolutionary tuning of controller parameters for the stabilization of selected discrete chaotic system, which is the two-dimensional Lozi map. The novelty of the approach is that the selected controlled discrete dissipative chaotic system is used within Chaos enhanced heuristic concept as the chaotic pseudo-random number generator to drive the mutation and crossover process in the DE. The idea was to utilize the hidden chaotic dynamics in pseudo-random sequences given by chaotic map to help Differential evolution algorithm in searching for the best controller settings for the same chaotic system. The optimizations were performed for three different required final behavior of the chaotic system, and two types of developed cost function. To confirm the robustness of presented approach, comparisons with canonical DE strategy and PSO algorithm have been performed.

All physical processes are deterministic de iure. Physicists speak about different types of determinism of physical processes, depending on the degree with which their course can be anticipated. Usually, the course of ergodic processes can be predicted with less certainty than the non-ergodic ones, the latter being integrable. Recent measurements of motions of single particles in composite systems, especially in living biological cells, show that such motions are, in most cases, breaking the Boltzmann’s ergodic hypothesis. On the other hand, their trajectories are random, i.e., one cannot know a priori where the particle will be even in near future. This leads to conclusion that many existing in nature processes are nonergodic but not integrable, therefore predictable only in the mean, representing still other type of determinism.

Application of chaotic signals in modern radar and telecommunications is an actual task that can significantly extend the functionality of these systems and improve their performance. In this paper, a method for information transmission using chaotic signal generated by nonlinear dynamical system with delayed feedback of ring type has been suggested. Modulating information sequence controls the parameter of non-linear element, so that it switches the chaotic modes and changes the spectral structure of the signal transmitted to the communication channel. A non-coherent reception was used for demodulation of the received message. The effectiveness of this method of information transmission for the covert operation of communication system in a complex interference environment has been shown.

We analyze the monthly sunspot number (SSN) data from January 1749 to June 2013. We use the Average Mutual Information and the False Nearest Neighbors methods to estimate the suitable embedding parameters. We calculate the correlation dimension to compute the dimension of the system’s attractor. The convergence of the correlation dimension to its true value, the positive largest Lyapunov exponent and the Recurrence Quantitative Analysis results provide evidences that the monthly SSN data exhibit deterministic chaotic behavior. The future prediction of monthly SSN is examined by using a neural network-type core algorithm. We perform ex-post predictions comparing them with the observed SSN values and the predictions published by the Solar Influences Data Analysis Center. It is shown that our technique is a better candidate for the prediction of the maximum monthly SSN value. We perform future predictions trying to forecast the maximum SSN value from July 2013 to June 2014. We show that the present cycle 24 is yet to peak. Finally, the negative economic impacts of maximum solar activity are discussed.

Simon's problem is one of the most important problems demonstrating the power of quantum computers. In this paper, we propose another exact quantum algorithm for solving Simon's problem with O ( n ) queries, which is simple, concrete and does not rely on special query oracles. Our algorithm combines Simon's algorithm with the quantum amplitude amplification technique to ensure its determinism. In particular, we show that Simon's problem can be solved by a classical deterministic algorithm with O ( 2 n ) queries (as we are aware, there were no classical deterministic algorithms for solving Simon's problem with O ( 2 n ) queries). Combining some previous results, we obtain the optimal separation in exact query complexities for Simon's problem: Θ ( n ) versus Θ ( 2 n ) . [ABSTRACT FROM AUTHOR]

Evidences from experimental measurements in tube banks submitted to turbulent cross flow in quadrangular and triangular arrangements show the presence of instabilities, being associated to the phenomenon of bistability, known in the simplified case of the flow on two cylinders side-by-side. Although not completely understood the study of the dynamic process of bistability can reveal new features about the chaotic behavior of these time series. As chaotic time series are observed routinely in experiments on physical systems, a study of the characteristics of bistability can be performed with the aid of techniques already established. This work presents a study about the determination of the Lyapunov exponents from experimental time series of bistable flows on the simplified geometry of two parallel circular cylinders and on a set of rows of a triangular tube bank. Time series of flow velocity and velocity fluctuations were obtained by means of the constant hot-wire anemometry technique in an aerodynamic channel. Discrete wavelet transform was used to make a multilevel decomposition of the series in several bandwidth values, accordingly with a selected decomposition level. Thus, the turbulence can be dissociated from the original signals, allowing a more accurate study to be conducted on the obtained state spaces. With these filtered time series, a state space reconstruction was performed by the method of time delays or Takens’ method, while the percentage of false neighbors together with the embedding dimension were useful for the choice of some of the analysis parameters. The Rosenstein’s method was applied to calculate the largest Lyapunov exponent of the time series. Easy to implement, this method is robust with respect to changes in most immersion parameters. Results show that the flow after two circular cylinders placed side-by-side and after two rows tube bank in triangular arrangement present positive largest Lyapunov exponents. This means that bistability has a clear chaotic behavior. In contrast, the flow after a five row tube bank is random. [ABSTRACT FROM AUTHOR]

Control and synchronization of fractional-order chaotic systems have attracted wide attention due to their numerous potential applications. To get suitable control method and parameters for fractional-order chaotic systems, the stability analysis of time-varying fractional-order systems should be discussed in the first place. Therefore, this paper analyzes the stability of the time-varying fractional-order systems and presents a stability theorem for the system with the order 0<α<1. This theorem is a sufficient condition which can discriminate the stability of time-varying systems conveniently. Feedback controllers are designed for control and synchronization of the fractional-order Lü chaotic system. The simulation results demonstrate the effectiveness of the proposed theorem. [ABSTRACT FROM AUTHOR]

In this paper, the benefits of channel-output feedback in the Gaussian interference channel (G-IC) are studied under the effect of additive Gaussian noise. Using a linear deterministic (LD) model, the signal to noise ratios (SNRs) in the feedback links beyond which feedback plays a significant role in terms of increasing the individual rates or the sum-rate are approximated. The relevance of this work lies in the fact that it identifies the feedback SNRs for which in any G-IC, one of the following statements is true: (a) feedback does not enlarge the capacity region; (b) feedback enlarges the capacity region and the sum-rate is greater than the largest sum-rate without feedback; and (c) feedback enlarges the capacity region but no significant improvement is observed in the sum-rate. [ABSTRACT FROM PUBLISHER]

Relevance of the researches is defined by the necessity to increase the efficiency of converters for the needs of renewable energy. The strict and conflicting requirements are often imposed to the control algorithms of DC voltage converters used in solar and wind power. The theory of deterministic chaos may be one of the ways of solving the problem of improving the algorithms. The aim of the research is to study and develop the control systems for DC-DC converters which allows working both in periodic mode and in deterministic chaos mode; to develop a physical model of DC-DC converter including the control system operating in deterministic chaos mode; make the voltage feedback circuit for stabilizing the output voltage at the given level. Research method: a review of patent and literature on the topic. The mathematical and experimental methods of investigation of the DC-DC converters were used. The method of mathematical modeling is based on preparation of electrical systems equations solution. The method of experimental research is based on the study of the output graphs, taken from the physical model of the DC-DC converters. Results. The authors have developed the physical model of the DC-DC converter with the control system operating in the deterministic chaos mode. The results show that the method of controlling the DC-DC converters with the help of deterministic chaos reduces electromagnetic interference, and improves significantly energy efficiency. The results obtained in the study can be used both at the stage of designing the power supplies in this class, and for further research and development of new control systems, including the control by deterministic chaos.

Objective: The aim of this article is to outline the role of chaotic dynamics in psychotherapy. Besides some empirical findings of chaos at different time scales, the focus is on theoretical modeling of change processes explaining and simulating chaotic dynamics. It will be illustrated how some common factors of psychotherapeutic change and psychological hypotheses on motivation, emotion regulation, and information processing of the client's functioning can be integrated into a comprehensive nonlinear model of human change processes.Methods: The model combines 5 variables (intensity of emotions, problem intensity, motivation to change, insight and new perspectives, therapeutic success) and 4 parameters into a set of 5 coupled nonlinear difference equations. The results of these simulations are presented as time series, as phase space embedding of these time series (i.e., attractors), and as bifurcation diagrams.Results: The model creates chaotic dynamics, phase transition-like phenomena, bi- or multi-stability, and sensibility of the dynamic patterns on parameter drift. These features are predicted by chaos theory and by Synergetics and correspond to empirical findings. The spectrum of these behaviors illustrates the complexity of psychotherapeutic processes.Conclusion: The model contributes to the development of an integrative conceptualization of psychotherapy. It is consistent with the state of scientific knowledge of common factors, as well as other psychological topics, such as: motivation, emotion regulation, and cognitive processing. The role of chaos theory is underpinned, not only in the world of computer simulations, but also in practice. In practice, chaos demands technologies capable of real-time monitoring and reporting on the nonlinear features of the ongoing process (e.g., its stability or instability). Based on this monitoring, a client-centered, continuous, and cooperative process of feedback and control becomes possible. By contrast, restricted predictability and spontaneous changes challenge the usefulness of prescriptive treatment manuals or other predefined programs of psychotherapy.

Abstract. The results of determination of parameters of dynamics of Caspian Sea level changes were studied. We determined quantities and dimensions of the phase space and the attractor, we calculated exponents of Lyapunov and assessed value of Kolmogorov – Sinai entropy based on analysis of time series by the change in the reservoir for 1931–2009.Introduction. When interpreting the data on oscillatory phenomena an application of the theory of self-organization approaches becomes interesting, as it allows to set in a certain extent the behavior and evolution of the system regardless the nature of occurring in them processes.Methods. During the preparation of article we applied a complex approach of nonlinear dynamics, consisting of the use of the discrete Fourier transform, the reconstruction of the dynamics of the time series with the construction of phase portraits and determining the dimensions of the phase space and attractor, calculation of Lyapunov exponents and Kolmogorov – Sinai entropy.Results. It is found that Fourier spectrum–discrete; attractor dimension is expressed in non-integer number, and it is more than three; dimension of the phase space is equal to five; values of Lyapunov exponents correspond to: λ1> 0, λ2 = 0, λ3< 0; KS-entropy value is greater than zero (h = 0,018 ± 0,002); characteristic time that can be predicted by changes in the level corresponding to 58 - 60 days.Conclusion. The analysis conducted by methods of nonlinear dynamics shows deterministic character of Caspian Sea level changes for 1931–2009 and realization of dynamic chaos.

The article presents the results of research on the prevalence of deterministic chaos during the formation of gas bubbles. In order to measure the time of the formation of gas bubbles a test bench was built. The research allowed us to determine the bifurcation diagrams for cylindrical and conical nozzles. Bifurcation occurs and it causes that we can see two points for the same gas stream. The system loses stability gradually until the appearance of chaos, i.e., the total instability of the system.[b]Keywords[/b]: deterministic chaos, bifurcation, bubbles

This paper presents an analytical study on the use of deterministic chaos as an entropy source for the generation of random numbers. The chaotic signal generated by a phase-locked loop (PLL) device is investigated using numerical simulations. Depending on the system parameters, the chaos originating from the PLL device can be either bounded or unbounded in the phase direction. Bounded and unbounded chaos differs in terms of the flatness of the power spectrum associated with the chaotic signal. Random bits are generated by regular sampling of the signal from bounded and unbounded chaos. A white Gaussian noise source is also sampled regularly to generate random bits. By varying the sampling frequency, and based on the autocorrelation and the approximate entropy analysis of the resulting bit sequences, a comparison is made between bounded chaos, unbounded chaos and Gaussian white noise as an entropy source for random number generators.

We investigate the various conditions that control the extinction and stability of a nonlinear mathematical spread model with stochastic perturbations. This model describes the spread of viruses into an infected computer network which is powered by a system of antivirus software. The system is analyzed by using the stability theory of stochastic differential equations and the computer simulations. First, we study the global stability of the virus-free equilibrium state and the virus-epidemic equilibrium state. Furthermore, we use the Itô formula and some other theoretical theorems of stochastic differential equation to discuss the extinction and the stationary distribution of our system. The analysis gives a sufficient condition for the infection to be extinct (i.e., the number of viruses tends exponentially to zero). The ergodicity of the solution and the stationary distribution can be obtained if the basic reproduction number Rp is bigger than 1, and the intensities of stochastic fluctuations are small enough. Numerical simulations are carried out to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

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Deterministic chaos is investigated for random dynamical systems in dimension one. Some well-known as well as new Li-Yorke-type theorems are randomized. Deterministic chaos exhibited by random dynamics is therefore called random chaos for brevity. Chaotic random dynamics are also studied for multivalued maps. [ABSTRACT FROM AUTHOR]

Recent developments toward a more holistic biology do not eliminate reductionism and determinism, but they do suggest more complex forms of them, in which there are multiple, interacting influences, as there are in complex or chaotic systems. Though there is a place in biology for both systemic and atomistic modes of explanation, for those with a theological perspective the shift to complex explanations in biology is often welcome. It suggests a more subtle view of divine action in which God's purposes are affected through engagement with the complex systems of creation rather than by discrete interventions. It also invites us to connect the biological interdependence with the interdependence in the nature and purposes of God, and it is consonant with a mystical vision of the unity of all things. [ABSTRACT FROM AUTHOR]

One of the simplest population biological models displaying a Hopf bifurcation is the Rosenzweig–MacArthur model with Holling type II response function as essential ingredient. In seasonally forced versions the fixed point on one side of the Hopf bifurcation becomes a limit cycle and the Hopf limit cycle on the other hand becomes a torus, hence the Hopf bifurcation becomes a torus bifurcation, and via torus destruction by further increasing relevant parameters can follow deterministic chaos. We investigate this route to chaos also in view of stochastic versions, since in real world systems only such stochastic processes would be observed. However, the Holling type II response function is not directly related to a transition from one to another population class which would allow a stochastic version straight away. Instead, a time scale separation argument leads from a more complex model to the simple 2 dimensional Rosenzweig–MacArthur model, via additional classes of food handling and predators searching for prey. This extended model allows a stochastic generalization with the stochastic version of a Hopf bifurcation, and ultimately also with additional seasonality allowing a torus bifurcation under stochasticity. Our study shows that the torus destruction into chaos with positive Lyapunov exponents can occur in parameter regions where also the time scale separation and hence stochastic versions of the model are possible. The chaotic motion is observed inside Arnol’d tongues of rational ratio of the forcing frequency and the eigenfrequency of the unforced Hopf limit cycle. Such torus bifurcations and torus destruction into chaos are also observed in other population biological systems, and were for example found in extended multi-strain epidemiological models on dengue fever. To understand such dynamical scenarios better also under noise the present low dimensional system can serve as a good study case. [ABSTRACT FROM AUTHOR]

Objective: The aim of this article is to outline the role of chaotic dynamics in psychotherapy. Besides some empirical findings of chaos at different time scales, the focus is on theoretical modeling of change processes explaining and simulating chaotic dynamics. It will be illustrated how some common factors of psychotherapeutic change and psychological hypotheses on motivation, emotion regulation, and information processing of the client's functioning can be integrated into a comprehensive nonlinear model of human change processes. Methods: The model combines 5 variables (intensity of emotions, problem intensity, motivation to change, insight and new perspectives, therapeutic success) and 4 parameters into a set of 5 coupled nonlinear difference equations. The results of these simulations are presented as time series, as phase space embedding of these time series (i.e., attractors), and as bifurcation diagrams. Results: The model creates chaotic dynamics, phase transition-like phenomena, bi- or multi-stability, and sensibility of the dynamic patterns on parameter drift. These features are predicted by chaos theory and by Synergetics and correspond to empirical findings. The spectrum of these behaviors illustrates the complexity of psychotherapeutic processes. Conclusion: The model contributes to the development of an integrative conceptualization of psychotherapy. It is consistent with the state of scientific knowledge of common factors, as well as other psychological topics, such as: motivation, emotion regulation, and cognitive processing. The role of chaos theory is underpinned, not only in the world of computer simulations, but also in practice. In practice, chaos demands technologies capable of real-time monitoring and reporting on the nonlinear features of the ongoing process (e.g., its stability or instability). Based on this monitoring, a client-centered, continuous, and cooperative process of feedback and control becomes possible. By contrast, restricted predictability and spontaneous changes challenge the usefulness of prescriptive treatment manuals or other predefined programs of psychotherapy. [ABSTRACT FROM AUTHOR]

We have investigated the scenarios of transition to chaos in the mathematical model of a genetic system constituted by a single transcription factor-encoding gene, the expression of which is self-regulated by a feedback loop that involves protein isoforms. Alternative splicing results in the synthesis of protein isoforms providing opposite regulatory outcomes - activation or repression. The model is represented by a differential equation with two delayed arguments. The possibility of transition to chaos dynamics via all classical scenarios: a cascade of period-doubling bifurcations, quasiperiodicity and type-I, type-II and type-III intermittencies, has been numerically demonstrated. The parametric features of each type of transition to chaos have been described. [ABSTRACT FROM AUTHOR]

To overcome the influence from deterministic type load disturbance with unknown dynamics, a bias-eliminated subspace identification method is proposed for consistent estimation. By decomposing the output response into three parts, deterministic, disturbed and stochastic components, in terms of the linear superposition principle, an LQ decomposition approach is developed to eliminate the disturbance and noise effect for unbiased estimation of the deterministic system state. Subsequently, a shift-invariant approach is given to retrieve the state matrices. Consistent estimation on the state matrices is analyzed with a proof. Illustrative example of open-loop system identification is shown to demonstrate the effectiveness and merit of the proposed method. [ABSTRACT FROM AUTHOR]

This paper gives the study of dynamics the Burridge-Knopoff spring-block model, assumed to represent a rockburst nucleation model along a shallow (near horizontal) thrust fault. The analysis is performed through numerical simulations of two models with different friction laws, modified by introduction the time delay τ in friction terms, which takes into account the delayed triggering effect of the mining excavation works. In the first model, a velocity dependent friction force is assumed. By introduction the time delay, the dynamics of one-block model shows a transition from equilibrium state to the periodic motion, with deterministic chaos as transient feature. In the second case, the model with the Dieterich-Ruina rate-and state- dependent friction law are examined. Increasing the time delay τ, the model exhibits a transition from equilibrium state, to periodic, quasiperiodic motion and chaos, for the certain parameter range. The obtained results indicate that the dynamics of rockburst nucleation model strongly depends on the nature of chosen friction law. It also confirms the fact that deterministic modeling is possible in the case of rockburst nucleation, since 'stochastic' motion is generated from the starting deterministic system.