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A dual‐core voltage‐controlled oscillator (VCO) using harmonic resonance is presented in this letter. Without an additional switch capacitor bank, harmonic resonance implemented in VCO is realized by only a single control voltage, satisfying the requirement of frequency‐modulated continuous‐wave radar. Two pairs of varactors are added to the transformer‐based tank, which ensures a constant ratio between the two resonant frequencies of the tank in the entire tuning range. Robustly single‐frequency oscillation is obtained by increasing the coupling coefficient of the transformer and the coupling capacitor's capacitance. Implemented in a 28‐nm complementary metal–oxide–semiconductor, the VCO shows a 14.75% frequency tuning range covering 34.16–39.6 GHz. The measured results show it exhibits −102.13 dBc/Hz phase noise at a 1 MHz offset from the 34.16 GHz. The oscillator core draws 21–28 mA from a 0.9 V supply. [ABSTRACT FROM AUTHOR]

In this work, we analyze the Kuramoto model (KM) with inertia on a convergent family of graphs. It is assumed that the intrinsic frequencies of the individual oscillators are sampled from a probability distribution. In addition, a given graph, which may also be random, assigns network connectivity. As in the original KM, in the model with inertia, the weak coupling regime features mixing, the state of the network when the phases (but not velocities) of all oscillators are distributed uniformly around the unit circle. We study patterns, which emerge when mixing loses stability under the variation of the strength of coupling. We identify a pitchfork (PF) and an Andronov–Hopf (AH) bifurcations in the model with multimodal intrinsic frequency distributions. To this effect, we use a combination of the linear stability analysis and Penrose diagrams, a geometric technique for studying stability of mixing. We show that the type of a bifurcation and a nascent spatiotemporal pattern depend on the interplay of the qualitative properties of the intrinsic frequency distribution and network connectivity. [ABSTRACT FROM AUTHOR]

Coordinated fluctuations in female reproductive physiology and thermoregulatory output have been reported for over a century. These changes occur rhythmically at the hourly (ultradian), daily (circadian), and multi-day (ovulatory) timescales, are critical for reproductive function, and have led to the use of temperature patterns as a proxy for female reproductive state. The mechanisms underlying coupling between reproductive and thermoregulatory systems are not fully established, hindering the expansion of inferences that body temperature can provide about female reproductive status. At present, numerous digital tools rely on temperature to infer the timing of ovulation and additional applications (e.g., monitoring ovulatory irregularities and progression of puberty, pregnancy, and menopause are developed based on the assumption that reproductive-thermoregulatory coupling occurs across timescales and life stages. However, without clear understanding of the mechanisms and degree of coupling among the neural substrates regulating temperature and the reproductive axis, whether such approaches will bear fruit in particular domains is uncertain. In this overview, we present evidence supporting broad coupling among the central circuits governing reproduction, thermoregulation, and broader systemic physiology, focusing on timing at ultradian frequencies. Future work characterizing the dynamics of reproductive-thermoregulatory coupling across the lifespan, and of conditions that may decouple these circuits (e.g., circadian disruption, metabolic disease) and compromise female reproductive health, will aid in the development of strategies for early detection of reproductive irregularities and monitoring the efficacy of fertility treatments. [ABSTRACT FROM AUTHOR]

Agricultural pests are increasingly appreciated as subjects of ecology. One particular case, a pest in coffee production, is analyzed here using the conceptual framework of complex systems, increasingly acknowledged as having an obvious home in the field of ecology, notorious for its complex structures. The particular case analyzed here arguably falls under the control of the complexity of the ecological system rather than of a simple magic bullet of population regulation. The system, which has been under study in southern Mexico for the past quarter century, is analyzed through the lens of neutral oscillations of the classical nondissipative Lotka-Volterra system. Based on three consumer/resource pairs (populations of [1] an ant, [2] a scale insect, [3] a beetle predator of the scale insect, [4] a fungal pathogen of the scale insect, and [5] a fly parasitoid of the ant), this five-dimensional system is well known qualitatively. Coupling all agents through both direct effects and trait-mediated indirect effects, the behavior of the neutral oscillation form of the system reveals a complex set of behaviors, including harmonized invariant sets, chaos, and/or quasiperiodicity. Such behaviors are well-known subjects in the science of complex systems and, it is argued, are ultimately sufficient to effect a degree of regulation on the pest, independent of explicit density-dependent feedback. Control of the system is thus seen as arguably actuated through its complexity, independent of any classic dissipative force. [ABSTRACT FROM AUTHOR]

Whereas topological symmetries have been recognized as crucially important to the exploration of synchronization patterns in complex networks of coupled dynamical oscillators, the identification of the symmetries in large-size complex networks remains as a challenge. Additionally, even though the topological symmetries of a complex network are known, it is still not clear how the system dynamics is transited among different synchronization patterns with respect to the coupling strength of the oscillators. We propose here the framework of eigenvector-based analysis to identify the synchronization patterns in the general complex networks and, incorporating the conventional method of eigenvalue-based analysis, investigate the emergence and transition of the cluster synchronization states. We are able to argue and demonstrate that, without a prior knowledge of the network symmetries, the method is able to predict not only all the cluster synchronization states observable in the network, but also the critical couplings where the states become stable and the sequence of these states in the process of synchronization transition. The efficacy and generality of the proposed method are verified by different network models of coupled chaotic oscillators, including artificial networks of perfect symmetries and empirical networks of non-perfect symmetries. The new framework paves a way to the investigation of synchronization patterns in large-size, general complex networks. [ABSTRACT FROM AUTHOR]

Introduction: In order to understand human hearing, it helps to understand how the ears of lower vertebrates, like, for instance, lizards, function. A key feature in common is that the ears of both humans and lizards emit faint, pure tones known as spontaneous otoacoustic emissions (SOAEs). More than four decades after their discovery, the mechanism underlying these emissions is still imperfectly understood, although it is known that they are important for improving the sensitivity and sharpness of hearing. In both humans and lizards, the frequencies of SOAEs change by a few percent when static pressure is applied to the tympanic membrane. For the human ear, this observation is normally explained by a so-called global oscillator model (such as with Shera's coherent reflection model), in which the emissions result from standing waves, and external pressure changes the boundary conditions – the stiffness of the oval and round windows – which then has a global effect on the SOAE frequencies. Methods: Here we investigate how changing parameters of an earlier developed local oscillator model for the lizard ear can change the frequencies of the SOAEs. A major feature of the model is that each oscillator is coupled only to its immediate neighbours. The oscillators then cluster into groups of identical frequency, and each of these so-called frequency plateaus can be taken to represent an SOAE. Results: Even though the natural (unperturbed) frequencies of all the oscillators remain fixed, here we find for several model parameters that by slightly changing their value the frequency plateaus – the SOAEs – shift by a few percent. Plots of how these changes alter SOAE frequencies are given, and their magnitude corresponds well with observations of SOAE changes in lizards. Discussion: Investigation of the influence of the change of parameters in an earlier developed local oscillator model for the lizard ear shows that a local oscillator model can explain small SOAE frequency changes as well as a global oscillator model. [ABSTRACT FROM AUTHOR]

Coordinated fluctuations in female reproductive physiology and thermoregulatory output have been reported for over a century. These changes occur rhythmically at the hourly (ultradian), daily (circadian), and multi-day (ovulatory) timescales, are critical for reproductive function, and have led to the use of temperature patterns as a proxy for female reproductive state. The mechanisms underlying coupling between reproductive and thermoregulatory systems are not fully established, hindering the expansion of inferences that body temperature can provide about female reproductive status. At present, numerous digital tools rely on temperature to infer the timing of ovulation and additional applications (e.g., monitoring ovulatory irregularities and progression of puberty, pregnancy, and menopause are developed based on the assumption that reproductive-thermoregulatory coupling occurs across timescales and life stages. However, without clear understanding of the mechanisms and degree of coupling among the neural substrates regulating temperature and the reproductive axis, whether such approaches will bear fruit in particular domains is uncertain. In this overview, we present evidence supporting broad coupling among the central circuits governing reproduction, thermoregulation, and broader systemic physiology, focusing on timing at ultradian frequencies. Future work characterizing the dynamics of reproductive-thermoregulatory coupling across the lifespan, and of conditions that may decouple these circuits (e.g., circadian disruption, metabolic disease) and compromise female reproductive health, will aid in the development of strategies for early detection of reproductive irregularities and monitoring the efficacy of fertility treatments.

We investigate how the structure of interactions between coupled oscillators influences the formation of asynchronous patterns in a multilayer network by formulating a simple, general multilayer oscillator model. We demonstrate the analysis of this model in three-oscillator systems, illustrating the role of interactions among oscillators in sustaining differences in both the phase and amplitude of oscillations leading to the formation of asynchronous patterns. Finally, we demonstrate the generalizability of our model's predictions through comparison with a more realistic multilayer model. Overall, our model provides a useful approach for predicting the types of asynchronous patterns that multilayer networks of coupled oscillators which cannot be achieved by the existing methods which focus on characterizing the synchronous state.

We investigate how the structure of interactions between coupled oscillators influences the formation of asynchronous patterns in a multilayer network by formulating a simple, general multilayer oscillator model. We demonstrate the analysis of this model in three-oscillator systems, illustrating the role of interactions among oscillators in sustaining differences in both the phase and amplitude of oscillations leading to the formation of asynchronous patterns. Finally, we demonstrate the generalizability of our model's predictions through comparison with a more realistic multilayer model. Overall, our model provides a useful approach for predicting the types of asynchronous patterns that multilayer networks of coupled oscillators which cannot be achieved by the existing methods which focus on characterizing the synchronous state.

Summary: Coupled tunnel‐diode oscillator lattice loops are investigated to characterize the mutual synchronization of nonlinear rotary pulses. In a properly biased lattice loop, a pulsed phase wave autonomously rotates. When two loops are coupled, these pulses are supposed to be mutually synchronized to start rotating with a fixed phase difference. To quantify the synchronization properties of both the in‐phase and out‐of‐phase rotary pulses, two five‐cell loops that are point‐coupled by a capacitor are studied using bifurcation analyses with respect to the bias voltage and coupling capacitance. In‐phase pulses are allowed irrespective of the coupling capacitance, whereas relatively small coupling is favorable for out‐of‐phase pulses. Moreover, a solution exists whose phase difference continuously varies with the bias voltage, which bifurcates from the out‐of‐phase pulses through pitchfork bifurcation. This study presents the result from the bifurcation analyses. For validation of the rotary pulse in the coupled loops, we measured a breadboarded test circuit in both the frequency and time domains. The in‐phase, out‐of‐phase, and symmetry‐broken rotary pulses were detected successfully. [ABSTRACT FROM AUTHOR]

We consider the escape of an initially excited dynamical system with two degrees of freedom from a potential well. Three different benchmark well potentials with different topologies are explored. The main challenge is to reveal the basic mechanisms that govern the escape in different regions of the parametric space and to construct appropriate asymptotic approximations for the analytic treatment of these mechanisms. In this study, numerical and analytical tools are used to classify and map the different escape mechanisms for various initial conditions and to offer the analytic criteria predicting the system's behavior for those cases. [ABSTRACT FROM AUTHOR]

Periodic Cheyne-Stokes breathing (CSB) oscillating between apnea and crescendo- decrescendo hyperpnea is the most common central apnea. Currently, there is no proven therapy for CSB, probably because the fundamental pathophysiological question of how the respiratory center generates this form of breathing instability is still unresolved. Therefore, we aimed to determine the respiratory motor pattern of CSB resulting from the interaction of inspiratory and expiratory oscillators and identify the neural mechanism responsible for breathing regularization induced by the supplemental CO2 administration. Analysis of the inspiratory and expiratory motor pattern in a transgenic mouse model lacking connexin-36 electrical synapses, the neonatal (P14) Cx36 knockout male mouse, with a persistent CSB, revealed that the reconfigurations recurrent between apnea and hyperpnea and vice versa result from cyclical turn on/off of active expiration driven by the expiratory oscillator, which acts as a master pacemaker of respiration and entrains the inspiratory oscillator to restore ventilation. The results also showed that the suppression of CSB by supplemental 12% CO2 in inhaled air is due to the stabilization of coupling between expiratory and inspiratory oscillators, which causes the regularization of respiration. CSB rebooted after washout of CO2 excess when the inspiratory activity depressed again profoundly, indicating that the disability of the inspiratory oscillator to sustain ventilation is the triggering factor of CSB. Under these circumstances, the expiratory oscillator activated by the cyclic increase of CO2 behaves as an "anti-apnea" center generating the crescendo--decrescendo hyperpnea and periodic breathing. The neurogenic mechanism of CSB identified highlights the plasticity of the twooscillator system in the neural control of respiration and provides a rationale base for CO2 therapy. [ABSTRACT FROM AUTHOR]

Undoubtedly, multistability represents one of the most followed venues for researchers working in the field of nonlinear science. Multistability refers to the situation where a combination of two or more attractors occurs for the same rank of parameters. However, to the best of our knowledge, the situation encountered in the relevant literature is never one where periodicity, chaos and hyperchaos coexist. In this article, we study a fourth-order autonomous dynamical system composing of a Duffing oscillator coupled to a van der Pol oscillator. Coupling consists in disturbing the amplitude of one oscillator with a signal proportional to the amplitude of the other. We exploit analytical and numerical methods (bifurcation diagrams, phase portraits, basins of attraction) to shed light on the plethora of bifurcation modes exhibited by the coupled system. Several ranks of parameters are revealed where the coupled system exhibits two or more competing behaviors. In addition to the transient dynamics, the most gratifying behavior reported in this article concerns the coexistence of four attractors consisting of a limit cycle of period-n, a pair of chaotic attractors and a hyperchaotic attractor. The impact of a fractional-order derivative is also examined. A physical implementation of the coupled oscillator system is performed and the PSpice simulations confirm the predictions of the theoretical study conducted in this work. [ABSTRACT FROM AUTHOR]

We study dynamics of a unidirectional ring of three Rulkov neurons coupled by chemical synapses. We consider both deterministic and stochastic models. In the deterministic case, the neural dynamics transforms from a stable equilibrium into complex oscillatory regimes (periodic or chaotic) when the coupling strength is increased. The coexistence of complete synchronization, phase synchronization, and partial synchronization is observed. In the partial synchronization state either two neurons are synchronized and the third is in antiphase, or more complex combinations of synchronous and asynchronous interaction occur. In the stochastic model, we observe noise-induced destruction of complete synchronization leading to multistate intermittency between synchronous and asynchronous modes. We show that even small noise can transform the system from the regime of regular complete synchronization into the regime of asynchronous chaotic oscillations. [ABSTRACT FROM AUTHOR]

This paper discusses the application of coupled reactance-less memristor-based oscillators (MBO) with binary output signals in oscillatory networks. A class of binary-coupled memristor oscillators provides simple integration with standard CMOS logic elements. Combining MBOs with binary logic elements ensures the operation of complex information processing algorithms. The analysis of the simplest networks based on MBOs is performed. The typical reactance-less MBO with current and potential inputs is considered. The output responses for input control signals are analyzed. It is shown that the current input signal impacts primarily the rate of memristor resistance variation, while the potential input signal changes the thresholds. The exploit of the potential input for the synchronization of coupled MBOs and current control input in order to provide the necessary encoding of information is suggested. The example of the application of coupled MBOs in oscillatory networks is given, and results of simulation are presented. [ABSTRACT FROM AUTHOR]

• The effect of the modulation signal on the dynamics of coupled Erbium-Doped Fiber Lasers is studied. • Two distinct clusters are formed in the non-modulated systems, which are lag-synchronized. • When the modulation signal is considered, the coupled systems can reach a chimera state. Studying the dynamics of coupled Erbium-Doped Fiber Lasers helps in optimizing the performance of these systems in different applications. An important factor in these systems is the modulation signal which can affect the dynamics of systems, leading to complex behaviors including diverse periodic and chaotic dynamics. This paper investigates the dynamics of a ring network of Erbium-Doped Fiber Lasers and compares its behaviors in the presence and absence of the modulation. The results reveal that although complete synchronization is not reachable, certain synchronization patterns exist during the periodic oscillations. In the non-modulated network, two distinct clusters are formed which can achieve lag synchronization under specific coupling intensities. While in the coupled modulated systems, the chimera state may form. These findings represent the complex relationship among modulation, coupling intensity, and network dynamics in EDFL systems. [ABSTRACT FROM AUTHOR]

The dynamics of coupled oscillators in a network are a significant topic in complex systems science. People with daily social rhythms interact through social networks in everyday life. This can be considered as a coupled oscillator in social networks, which is also true in online society (online social rhythms). Controlling online social rhythms can contribute to healthy daily rhythms and mental health. We consider controlling online social rhythms by introducing periodic forcing (pacemakers). However, theoretical studies predict that pacemaker effects do not spread widely across mutually connected networks such as social networks. We aimed to investigate the characteristics of the online social rhythms with pacemakers on an empirical online social network. Therefore, we conducted an intervention experiment on the online social rhythms of hundreds of players (participants who were pacemakers) using an avatar communication application ( N = 416). We found that the intervention had little effect on neighbors’ online social rhythms. This may be because mutual entrainment stabilizes the neighbors’ and their friends’ rhythms. That is, their online social rhythms were stable despite the disturbances. However, the intervention affected on neighbors’ rhythms when a participant and their neighbor shared many friends. This suggests that interventions to densely connected player groups may make their and their friends’ rhythms better. We discuss the utilization of these properties to improve healthy online social rhythms.

Periodic Cheyne–Stokes breathing (CSB) oscillating between apnea and crescendo–decrescendo hyperpnea is the most common central apnea. Currently, there is no proven therapy for CSB, probably because the fundamental pathophysiological question of how the respiratory center generates this form of breathing instability is still unresolved. Therefore, we aimed to determine the respiratory motor pattern of CSB resulting from the interaction of inspiratory and expiratory oscillators and identify the neural mechanism responsible for breathing regularization induced by the supplemental CO2 administration. Analysis of the inspiratory and expiratory motor pattern in a transgenic mouse model lacking connexin-36 electrical synapses, the neonatal (P14) Cx36 knockout male mouse, with a persistent CSB, revealed that the reconfigurations recurrent between apnea and hyperpnea and vice versa result from cyclical turn on/off of active expiration driven by the expiratory oscillator, which acts as a master pacemaker of respiration and entrains the inspiratory oscillator to restore ventilation. The results also showed that the suppression of CSB by supplemental 12% CO2 in inhaled air is due to the stabilization of coupling between expiratory and inspiratory oscillators, which causes the regularization of respiration. CSB rebooted after washout of CO2 excess when the inspiratory activity depressed again profoundly, indicating that the disability of the inspiratory oscillator to sustain ventilation is the triggering factor of CSB. Under these circumstances, the expiratory oscillator activated by the cyclic increase of CO2 behaves as an “anti-apnea” center generating the crescendo–decrescendo hyperpnea and periodic breathing. The neurogenic mechanism of CSB identified highlights the plasticity of the two-oscillator system in the neural control of respiration and provides a rationale base for CO2 therapy.

This paper is concerned with periodic solutions of coupled oscillators. A systematic method of existence and stability of periodic solutions for coupled oscillators is provided in a combined method of graph theory, coincidence degree theory and Lyapunov method. Sufficient conditions for periodicity are obtained, which can be easily checked in the real applications. Finally, a numerical example is also provided to illustrate the correctness of theoretical results. [ABSTRACT FROM AUTHOR]

In this investigation, two different models for two coupled asymmetrical oscillators, known as, coupled forced damped Duffing oscillators (FDDOs) are reported. The first model of coupled FDDOs consists of a nonlinear forced damped Duffing oscillator (FDDO) with a linear oscillator, while the second model is composed of two nonlinear FDDOs. The Krylov–Bogoliubov–Mitropolsky (KBM) method, is carried out for analyzing the coupled FDDOs for any model. To do that, the coupled FDDOs are reduced to a decoupled system of two individual FDDOs using a suitable linear transformation. After that, the KBM method is implemented to find some approximations for both unforced and forced damped Duffing oscillators (DDOs). Furthermore, the KBM analytical approximations are compared with the fourth-order Runge–Kutta (RK4) numerical approximations to check the accuracy of all obtained approximations. Moreover, the RK4 numerical approximations to both coupling and decoupling systems of FDDOs are compared with each other. [ABSTRACT FROM AUTHOR]

The functionalization of internal resonance (IR) is theoretically and experimentally demonstrated on a nonlinear hybrid vibration energy harvester (HVEH) based on piezoelectric (PE) and electromagnetic (EM) transductions. This nonlinear phenomenon is tuned by adjusting the gaps between the moving magnets of the structure, enabling 1:1 and 2:1 IR. The experimental results prove that the activation of 2:1 IR with a realistic excitation amplitude allows the improvement of both the frequency bandwidth (BW) and the harvested power (HP) by 300 % and 100 % , respectively compared to the case away from IR. These remarkable results open the way towards a very large scale integration of coupled resonators with simultaneous internal resonances. [ABSTRACT FROM AUTHOR]

The effect of topological disorder on the dynamic behaviour of topologically constrained oscillator chains is investigated through a normal mode analysis. A measure for mode localization based on the skewness of the density of energy states of normal modes is proposed, which correlates well with main configuration characteristics. Appropriate configuration sampling is achieved by employing the Ising model together with the Metropolis algorithm. [ABSTRACT FROM AUTHOR]

A resonant pulse transformer with shock excitation is compared with a system of coupled pendulums with different masses tuned to resonance. For the Tesla transformer and coupled pendulums, conditions for complete energy transfer during one-half of the beat cycle were obtained. The requirements for the system parameters and initial conditions necessary for complete transfer of energy in the case of two spring-coupled pendulums with different masses and of the same length were first determined theoretically and then verified experimentally. The dependence of the minimum time for complete transfer of energy from one pendulum to the other on the system parameters is obtained. [ABSTRACT FROM AUTHOR]

The world view of rodents is largely determined by sensation on two length scales. One is within the animal's peri-personal space; sensorimotor control on this scale involves active movements of the nose, tongue, head, and vibrissa, along with sniffing to determine olfactory clues. The second scale involves the detection of more distant space through vision and audition; these detection processes also impact repositioning of the head, eyes, and ears. Here we focus on orofacial motor actions, primarily vibrissa-based touch but including nose twitching, head bobbing, and licking, that control sensation at short, peri-personal distances. The orofacial nuclei for control of the motor plants, as well as primary and secondary sensory nuclei associated with these motor actions, lie within the hindbrain. The current data support three themes: First, the position of the sensors is determined by the summation of two drive signals, i.e., a fast rhythmic component and an evolving orienting component. Second, the rhythmic component is coordinated across all orofacial motor actions and is phase-locked to sniffing as the animal explores. Reverse engineering reveals that the preBötzinger inspiratory complex provides the reset to the relevant premotor oscillators. Third, direct feedback from somatosensory trigeminal nuclei can rapidly alter motion of the sensors. This feedback is disynaptic and can be tuned by high-level inputs. A holistic model for the coordination of orofacial motor actions into behaviors will encompass feedback pathways through the midbrain and forebrain, as well as hindbrain areas.

We consider a model for an N × N lattice network of weakly coupled neural oscilla- tors with periodic boundary conditions (2D square torus), where the coupling between neurons is assumed to be within a von Neumann neighborhood of size r, denoted as von Neumann r-neighborhood. Using the phase model reduction technique, we study the existence of cluster solutions with constant phase differences (Ψh, Ψv) between adjacent oscillators along the horizontal and vertical directions in our network, where Ψh and Ψv are not necessarily to be identical. Applying the Kronecker production representation and the circulant matrix theory, we develop a novel approach to analyze the stability of cluster solutions with constant phase difference (i.e., Ψh,Ψv are equal). We begin our analysis by deriving the precise conditions for stability of such cluster solutions with von Neumann 1-neighborhood and 2 neighborhood couplings, and then we generalize our result to von Neumann r-neighborhood coupling for arbitrary neighborhood size r ≥ 1. This developed approach for the stability analysis indeed can be extended to an arbitrary coupling in our network. Finally, numerical simulations are used to validate the above analytical results for various values of N and r by considering an inhibitory network of Morris-Lecar neurons.

• Fractional-order Stuart-Landau oscillators with nonisochronicity parameter are investigated. • Nonisochronicity parameter can induce the swing of synchronization mediated by chimera state. • The effect of the fractional derivatives on synchronization transition is revealed. In this letter, we investigate the various dynamical behaviors in fractional-order coupled Stuart-Landau oscillator networks with the nonisochronicity parameter. We find that the nonisochronicity parameter can induce the swing of synchronization mediated by the imperfect synchronized state and the amplitude cluster state, and we verify the accuracy of the emergence of the swing of synchronization by the strength of incoherence and stability theory. Moreover, we discuss the effects of different parameters on the swing of synchronization mediated by the chimera state. First, as the nonisochronicity parameter increases, the range of the swing increases. Second, the decreasing of fractional-order derivative will lead to the reduction in the range of swing intervals. Third, the system exhibits the swing of synchronization mediated by the imperfect synchronized state when different initial conditions are employed. In particular, the system can show the imperfect breathing chimera state under symmetric initial conditions. [ABSTRACT FROM AUTHOR]

We consider a ring of phase oscillators interacting with distance-dependent time delays in general forms. It is found that the distance-dependent interaction delay is an essential driving mechanism for the twisted state to occur as a generic state. We carry out rigorous stability analysis for the existence and stability of the twisted states along the Ott–Antonsen invariant manifold and derive the exact characteristic equations for the stability conditions for arbitrarily chosen distance-dependent delay function. The complete stability diagrams are illustrated for two types of distance-dependent delay schemes, the propagational and step-wise interaction delays. Our theoretical results are verified using the direct numerical simulations of the model system. • Low-dimensional dynamics of oscillator system with distance-dependent time delays is found along the Ott–Antonsen invariant manifold. • Exact characteristic equations for the stability conditions for arbitrary distance-dependent delays are derived. • Complete stability diagrams are illustrated for two types of distance-dependent delay schemes. [ABSTRACT FROM AUTHOR]

In this work, we present a parsimonious set of ordinary differential equations (ODEs), describing with good precision and over a wide range of frequencies the linear and nonlinear dynamics of different types of fully premixed, turbulent, swirl-stabilized flames. This phenomenological model comprises eight ODEs and can physically be interpreted as a superposition of two mass–spring–damper systems. The model is characterized by 11 parameters and one nonlinear term of structure β x 2 x ̇ in particular, with position x and rate of displacement x ̇ of a given oscillator mass. The model can be optimized in frequency domain or in time domain. The former is suitable for situations where experimental data of the flame transfer function (FTF) and flame describing function (FDF) are available. The latter is suitable for situations where time series (input and output) from numerical simulations or experiments are available. In the present work, large eddy simulation (LES) data is used. Choosing a model comprising ODEs enables us to describe the dynamics of the flame using linear and nonlinear input-to-output transformations via the states. This is a sharp contrast to commonly applied finite impulse response (FIR) models, which can only directly employ nonlinear functions acting on the input or output — not on derivatives or other states of the underlying dynamical system. We demonstrate the simplicity of implementing our model by investigating the coupling of a time-domain acoustic solver with the set of ODEs proposed, all within the graphical interface of Simulink. The x 2 x ̇ nonlinearity plays a crucial role in achieving good agreement in the nonlinear regime, as observed in the FDF, as well as in both the amplitude and frequency of the investigated limit cycle, which exhibits a simple period-one oscillation. However, there is still room for improvement in the nonlinear model if more complex dynamics need to be modeled, thanks to the flexible ODE structure proposed in this work. Novelty and significance A phenomenological model, characterized by a parsimonious set of ordinary differential equations is presented. This model is able to describe the dynamic flame response of typical turbulent, swirl-stabilized flames to acoustic disturbances in their linear and nonlinear regime. The model can be calibrated from broadband time series data or reference frequency domain data. After calibration, the model can be coupled to an acoustic network to predict the occurrence of limit cycles and (if they are present) their frequency as well as amplitude. • We propose a parsimonious system of ODEs for flame response modeling • The system of ODEs describes the flame response of typical turbulent swirled flames • Model parameters are calibrated using frequency domain data or time series data • In the linear regime the model performs comparably to established FIR techniques • In the nonlinear regime, the model qualitatively recovers the FDF • We demonstrate how to couple the nonlinear model to an acoustic network • Using a combination of model and acoustic network, simple limit cycles are recovered • The proposed model can be understood as the superposition of two subsystems • Each subsystem characterizes the flame's response to swirl or axial fluctuations [ABSTRACT FROM AUTHOR]

Biological processes are governed by the expression of proteins, and for some proteins, their level of expression can fluctuate periodically over time (i.e., they oscillate). Many oscillatory proteins (e.g., cell cycle proteins and those from the HES family of transcription factors) are connected in complex ways, often within large networks. This complexity can be elucidated by developing intuitive mathematical models that describe the underlying critical aspects of the relationships between these processes. Here, we provide a mathematical explanation of a recently discovered biological phenomenon: the phasic position of the gene Hes1's oscillatory expression at the beginning of the cell cycle of an individual human breast cancer stem cell can have a predictive value on how long that cell will take to complete a cell cycle. We use a two-component model of coupled oscillators to represent Hes1 and the cell cycle in the same cell with minimal assumptions. Inputting only the initial phase angles, we show that this model is capable of predicting the dynamic mitosis to mitosis behaviour of Hes1 and predicting cell cycle length patterns as found in real-world experimental data. Moreover, we discover that bidirectional coupling between Hes1 and the cell cycle is critical within the system for the data to be reproduced and that nonfixed asymmetry in the interactions between the oscillators is required. The phase dynamics we present here capture the complex interplay between Hes1 and the cell cycle, helping to explain nongenetic cell cycle variability, which has critical implications in cancer treatment contexts. [ABSTRACT FROM AUTHOR]

In this paper we investigate the stability of the null solution of a system of ODEs describing the motion of two coupled damped nonlinear oscillators. We also show that for any solution (x; y) of the system we have limt!+1 x (t) = limt!+1 x_ (t) = limt!+1 y (t) = limt!+1 y_ (t) = 0; for small initial data in the case when the uniqueness of solutions is not guaranteed. Our proofs are mainly based on a generalized form of Schauder-Tychonoff fixed point theorem. The theoretical results are illustrated with numerical simulations. [ABSTRACT FROM AUTHOR]

In this letter, we propose a compact frequency programmable oscillator with an NbO2-based insulator-metal transition (IMT) device and three-terminal Li-based electro-chemical RAM (Li-ECRAM) for coupled oscillators-based temporal pattern recognition system. Owing to the non-volatility, multilevel characteristics, and linear conductance modulation of Li-ECRAM, our proposed oscillator exhibits a large number of programmable frequencies (~45) and high controllability by applying pulses to the Li-ECRAM to attain the target frequency. Furthermore, we demonstrated injection locking phenomenon in our proposed oscillators, which can be utilized for the frequency detection of the injected signal. Finally, we simulated four-coupled oscillators system for the frequency classification of the input temporal signal with multiple frequencies and amplitude noise. These results demonstrate the feasibility of a temporal pattern recognition system composed of our proposed compact frequency-programmable oscillators. [ABSTRACT FROM AUTHOR]

The reciprocity theorem in elastic materials states that the response of a linear, time-invariant system to an external load remains invariant with respect to interchanging the locations of the input and output. In the presence of nonlinear forces within a material, circumventing the reciprocity invariance requires breaking the mirror symmetry of the medium, thus allowing different wave propagation characteristics in opposite directions along the same transmission path. This work highlights the application of numerical continuation methods for exploring the steady-state nonreciprocal dynamics of nonlinear periodic materials in response to external harmonic drive. Using the archetypal example of coupled oscillators, we apply continuation methods to analyze the influence of nonlinearity and symmetry on the reciprocity invariance. We present symmetry-breaking bifurcations for systems with and without mirror symmetry, and discuss their influence on the nonreciprocal dynamics. Direct computation of the reciprocity bias allows the identification of response regimes in which nonreciprocity manifests itself as a phase shift in the output displacements. Various operating regimes, bifurcations and manifestations of nonreciprocity are identified and discussed throughout the work. [ABSTRACT FROM AUTHOR]

Background: An earlier oscillator model for the generation of spontaneous otoacoustic emissions (SOAEs) from the lizard ear is extended with a connection of the oscillators to the basilar papilla, to make it possible that these SOAEs can be transported to the tympanic membrane, to be emitted. Material and methods: The generators of spontaneous otoacoustic emissions are modelled as a one-dimensional array of Hopf-resonators. The resonators (or oscillators) are coupled to their neighbours, and to the basilar papilla. The papilla is modelled as a rigid structure, that is flexibly connected to its surroundings. Results: Frequency spectra are given for different sets of coupling parameters, both for nearest neighbour coupling of the oscillators, and for coupling to the papilla, and also after the introduction of irregularities in the damping of the oscillators. Waterfall and density plots show clustering of the oscillators in frequency plateaus, and entrainment of a cluster of oscillators by an externally applied sinusoidal force. All these model outcomes correspond with characteristics of SOAEs emitted by real lizard ears. Conclusions: The present model is a useful extension of an earlier model. Because its characteristics differ from that of a model that is used to describe the generation of SOAEs by mammalian ears, it revives the discussion whether different models are needed for SOAE generation in different animal species [ABSTRACT FROM AUTHOR]

Non-stationary feature information is common in engineering applications, and its signal features are irregular compared to stationary signals. Because of its strong volatility, the traditional signal analysis method is no longer applicable. In some environments, strong background noise makes it difficult to extract feature information. Adaptive cascade stochastic resonance is an effective method to enhance the stationary signal. The weak characteristic signal is enhanced step by step, but it is difficult to extract non-stationary information under strong noise background. Compared with the classical bistable system, the piecewise linear system can overcome the disadvantage of output saturation and has high output signal-to-noise ratio. Therefore, an adaptive cascaded stochastic resonance method is proposed to extract and enhance the non-stationary weak feature information. Firstly, the simulated non-stationary signal of a faulty bearing is preprocessed. The non-stationary feature information is transformed into the stationary feature information by computed order analysis method. Combined with maximum correlation kurtosis deconvolution filtering, the periodic feature of the characteristic signal is highlighted. Then, the adaptive stochastic resonance in a piecewise linear system and variational mode decomposition are applied to enhance characteristic signal and reduce noise interference. The cascaded mechanism is used to filter the interference signal and enhance the characteristic information step by step. Finally, the effectiveness of the method is verified by experimental signals, which can significantly improve the output characteristic amplitude and signal-to-noise ratio. [ABSTRACT FROM AUTHOR]

Embryonic development hinges on effective coordination of molecular events across space and time. Waves have recently emerged as constituting an ubiquitous mechanism that ensures rapid spreading of regulatory signals across embryos, as well as reliable control of their patterning, namely, for the emergence of body plan structures. In this article, we review a selection of recent quantitative work on signaling waves and present an overview of the theory of waves. Our aim is to provide a succinct yet comprehensive guiding reference for the theoretical frameworks by which signaling waves can arise in embryos. We start, then, from reaction–diffusion systems, both static and time dependent; move to excitable dynamics; and conclude with systems of coupled oscillators. We link these theoretical models to molecular mechanisms recently elucidated for the control of mitotic waves in early embryos, patterning of the vertebrate body axis, micropattern cultures, and bone regeneration. Our goal is to inspire experimental work that will advance theory in development and connect its predictions to quantitative biological observations. [ABSTRACT FROM AUTHOR]