Noise enhanced phase synchronization and coherence resonance in sets of chaotic oscillators with weak global coupling

The effect of noise on phase synchronization in small sets and larger populations of weakly coupled chaotic oscillators is explored. Both independent and correlated noise are found to enhance phase synchronization of two coupled chaotic oscillators below the synchronization threshold; this is in contrast to the behavior of two coupled periodic oscillators. This constructive effect of noise results from the interplay between noise and the locking features of unstable periodic orbits. We show that in a population of nonidentical chaotic oscillators, correlated noise enhances synchronization in the weak coupling region. The interplay between noise and weak coupling induces a collective motion in which the coherence is maximal at an optimal noise intensity. Both the noise-enhanced phase synchronization and the coherence resonance numerically observed in coupled chaotic R?ssler oscillators are verified experimentally with an array of chaotic electrochemical oscillators.     

Synchronization of chaotic oscillator time scales

We consider chaotic oscillator synchronization and propose a new approach for detecting the synchronized behavior of chaotic oscillators. This approach is based on analysis of different time scales in the time series generated by coupled chaotic oscillators. We show that complete synchronization, phase synchronization, lag synchronization, and generalized synchronization are particular cases of the synchronized behavior called time-scale synchronization. A quantitative measure of chaotic oscillator synchronous behavior is proposed. This approach is applied to coupled Rössler systems.     

Phase synchronization in ensembles of bursting oscillators

We study the effects of mutual and external chaotic phase synchronization in ensembles of bursting oscillators. These oscillators (used for modeling neuronal dynamics) are essentially multiple time scale systems. We show that a transition to mutual phase synchronization takes place on the bursting time scale of globally coupled oscillators, while on the spiking time scale, they behave asynchronously. We also demonstrate the effect of the onset of external chaotic phase synchronization of the bursting behavior in the studied ensemble by a periodic driving applied to one arbitrarily taken neuron. We also propose an explanation of the mechanism behind this effect. We infer that the demonstrated phenomenon can be used efficiently for controlling bursting activity in neural ensembles.     

Locking-based frequency measurement and synchronization of chaotic oscillators with complex dynamics

We propose a method for the determination of a characteristic oscillation frequency for a broad class of chaotic oscillators generating complex signals. It is based on the locking of standard periodic self-sustained oscillators by an irregular signal. The method is applied to experimental data from chaotic electrochemical oscillators, where other approaches of frequency determination (e.g., based on Hilbert transform) fail. Using the method we characterize the effects of phase synchronization for systems with ill-defined phase by external forcing and due to mutual coupling.     

环形耦合Duffing振子间的同步突变

以环形耦合Duffing振子系统为研究对象,分析了耦合振子间的同步演化过程.发现在弱耦合条件下,如果所有振子受到同一周期策动力的驱动,那么系统在经历倍周期分岔、混沌态、大尺度周期态的相变时,各振子的运动轨迹之间将出现由同步到不同步再到同步的两次突变现象.利用其中任何一次同步突变现象可以实现系统相变的快速判别,并由此补充了利用倍周期分岔与混沌态的这一相变对微弱周期信号进行检测的方法. 关键词： Duffing振子 同步突变 相变 微弱信号检测     

Experimental investigation of high-quality synchronization of coupled oscillators

We describe two experiments in which we investigate the synchronization of coupled periodic oscillators. Each experimental system consists of two identical coupled electronic periodic oscillators that display bursts of desynchronization events similar to those observed previously in coupled chaotic systems. We measure the degree of synchronization as a function of coupling strength. In the first experiment, high-quality synchronization is achieved for all coupling strengths above a critical value. In the second experiment, no high-quality synchronization is observed. We compare our results to the predictions of the several proposed criteria for synchronization. We find that none of the criteria accurately predict the range of coupling strengths over which high-quality synchronization is observed. (c) 2000 American Institute of Physics.     

An approach to chaotic synchronization

This paper deals with the chaotic oscillator synchronization. An approach to the synchronization of chaotic oscillators has been proposed. This approach is based on the analysis of different time scales in the time series generated by the coupled chaotic oscillators. It has been shown that complete synchronization, phase synchronization, lag synchronization, and generalized synchronization are the particular cases of the synchronized behavior called "time-scale synchronization." The quantitative measure of chaotic oscillator synchronous behavior has been proposed. This approach has been applied for the coupled R?ssler systems and two coupled Chua's circuits.     

Alternate Phase Synchronization in Coupled Chaotic Oscillators

Phase locking dynamics in coupled chaotic oscillators is investigated.For chaotic systems with a poorly coherent phase variable,the imperfect phase locking can be observed befor the onset of a complete phase synchronization.The temporal alternations among n:n phase lockings are found,which originate from an overlap of m:n Arnold tongues.     

Intermittent lag synchronization in a driven system of coupled oscillators

We study intermittent lag synchronization in a system of two identical mutually coupled Duffing oscillators with parametric modulation in one of them. This phenomenon in a periodically forced system can be seen as intermittent jump from phase to lag synchronization, during which the chaotic trajectory visits a periodic orbit closely. We demonstrate different types of intermittent lag synchronizations, that occur in the vicinity of saddle-node bifurcations where the system changes its dynamical state, and characterize the simplest case of period-one intermittent lag synchronization.     

Automatic control of phase synchronization in coupled complex oscillators

We present an automatic control method for phase locking of regular and chaotic nonidentical oscillations, when all subsystems interact via feedback. This method is based on the well known principle of feedback control which takes place in nature and is successfully used in engineering. In contrast to unidirectional and bidirectional coupling, the approach presented here supposes the existence of a special controller, which allows to change the parameters of the controlled systems. First we discuss general principles of automatic phase synchronization (PS) for arbitrary coupled systems with a controller whose input is given by a special quadratic form of coordinates of the individual systems and its output is a result of the application of a linear differential operator. We demonstrate the effectiveness of our approach for controlled PS on several examples: (i) two coupled regular oscillators, (ii) coupled regular and chaotic oscillators, (iii) two coupled chaotic Rössler oscillators, (iv) two coupled foodweb models, (v) coupled chaotic Rössler and Lorenz oscillators, (vi) ensembles of locally coupled regular oscillators, (vii) ensembles of locally coupled chaotic oscillators, and (viii) ensembles of globally coupled chaotic oscillators.     

Noise-enhanced phase synchronization of chaotic oscillators

The effects of noise on phase synchronization (PS) of coupled chaotic oscillators are explored. In contrast to coupled periodic oscillators, noise is found to enhance phase synchronization significantly below the threshold of PS. This constructive role of noise has been verified experimentally with chaotic electrochemical oscillators of the electrodissolution of Ni in sulfuric acid solution.     

Isochronal synchronization in networks and chaos-based TDMA communication

Pairs of delay-coupled chaotic systems were shown to be able to achieve isochronal synchronization under bidirectional coupling and self-feedback. Such identical-in-time behavior was demonstrated to be stable under a set of conditions and to support simultaneous bidirectional communication between pairs of chaotic oscillators coupled with time-delay. More recently, it was shown that isochronal synchronization can emerge in networks with several hundreds of oscillators, which allows its exploitation for communication in distributed systems. In this paper, we introduce a conceptual framework for the application of isochronal synchronization to TDMA communication in networks of delay-coupled chaotic oscillators. On the basis of the stable and identical-in-time behavior of delay-coupled chaotic systems, the chaotic dynamics of distributed oscillators is used to support and sustain coordinate communication among nodes over the network. On the basis of the unique features of chaotic systems in isochronal synchronization, the chaotic signals are used to timestamp clock readings at the physical layer such that logical clock synchronization among the nodes (a prerequisite for TDMA) can be exploited using the same basic structure. The result is a standalone network communication scheme that can be advantageously applied in the context of ad-hoc networks or alike, especially short-ranged ones that yield low values of time-delay. As explored to its depths in practical implementations, this conceptual framework is argued to have potential to provide gain in simplicity, security and efficiency in communication schemes for autonomous/standalone network applications.     

The effect of finite response–time in coupled dynamical systems

The paper investigates synchronization in unidirectionally coupled dynamical systems wherein the influence of drive on response is cumulative: coupling signals are integrated over a time interval τ. A major consequence of integrative coupling is that the onset of the generalized and phase synchronization occurs at higher coupling compared to the instantaneous (τ?=?0) case. The critical coupling strength at which synchronization sets in is found to increase with τ. The systems explored are the chaotic Rössler and limit cycle (the Landau–Stuart model) oscillators. For coupled Rössler oscillators the region of generalized synchrony in the phase space is intercepted by an asynchronous region which corresponds to anomalous generalized synchronization.     

The effect of time-delay on anomalous phase synchronization

Anomalous phase synchronization in nonidentical interacting oscillators is manifest as the increase of frequency disorder prior to synchronization. We show that this effect can be enhanced when a time-delay is included in the coupling. In systems of limit-cycle and chaotic oscillators we find that the regions of phase disorder and phase synchronization can be interwoven in the parameter space such that as a function of coupling or time-delay the system shows transitions from phase ordering to disorder and back.     

Two scenarios of breaking chaotic phase synchronization

Two types of phase synchronization (accordingly, two scenarios of breaking phase synchronization) between coupled stochastic oscillators are shown to exist depending on the discrepancy between the control parameters of interacting oscillators, as in the case of classical synchronization of periodic oscillators. If interacting stochastic oscillators are weakly detuned, the phase coherency of the attractors persists when phase synchronization breaks. Conversely, if the control parameters differ considerably, the chaotic attractor becomes phase-incoherent under the conditions of phase synchronization break.     

Open-loop frequency response for a chaotic masking system

In this paper, a new numerical simulation approach is proposed for the study of open-loop frequency response of a chaotic masking system. Using Chua's circuit and the Lorenz system as illustrative examples, we have shown that one can employ chaos synchronization to separate the feedback network from a chaotic masking system, and then use numerical simulation to obtain the open-loop synchronization response, the phase response, and the amplitude response of a chaotic masking system. Based on the analysis of the frequency response, we have also proved that changing the amplitude of the exciting (input) signal within normal working domain does not influence the frequency response of the chaotic masking system. The new numerical simulation method developed in this paper can be extended to consider the open-loop frequency response of other systems described by differential or difference equations.     

Chaotic phase synchronization in small-world networks of bursting neurons

We investigate the chaotic phase synchronization in a system of coupled bursting neurons in small-world networks. A transition to mutual phase synchronization takes place on the bursting time scale of coupled oscillators, while on the spiking time scale, they behave asynchronously. It is shown that phase synchronization is largely facilitated by a large fraction of shortcuts, but saturates when it exceeds a critical value. We also study the external chaotic phase synchronization of bursting oscillators in the small-world network by a periodic driving signal applied to a single neuron. It is demonstrated that there exists an optimal small-world topology, resulting in the largest peak value of frequency locking interval in the parameter plane, where bursting synchronization is maintained, even with the external driving. The width of this interval increases with the driving amplitude, but decrease rapidly with the network size. We infer that the externally applied driving parameters outside the frequency locking region can effectively suppress pathologically synchronized rhythms of bursting neurons in the brain.     

Analysis of phase synchronization of chaotic oscillations in terms of symbolic CTQ-analysis

The application of symbolic CTQ-analysis for studying synchronization of chaotic oscillations is considered. This approach differs substantially from its analogs since it makes it possible to diagnose and measure quantitatively the characteristics of intermittency regimes in synchronization of chaotic systems and, hence, to analyzer the temporal structure of synchronization. The application of the symbolic analysis apparatus based on the T alphabet to systems with phase locking and synchronization of time scales is demonstrated for the first time. As an example, a complex system of two mutually coupled nonidentical Rössler oscillators in the helical chaos regime with attractors having an ill-conditioned phase is considered. The results show that the method considered here makes it possible to reliably diagnose synchronism sooner than a phase locking and/or time-scale synchronization threshold is detected.     

Anticipating, complete and lag synchronizations in RC phase-shift network based coupled Chua's circuits without delay

We construct a new RC phase shift network based Chua's circuit, which exhibits a period-doubling bifurcation route to chaos. Using coupled versions of such a phase-shift network based Chua's oscillators, we describe a new method for achieving complete synchronization (CS), approximate lag synchronization (LS), and approximate anticipating synchronization (AS) without delay or parameter mismatch. Employing the Pecora and Carroll approach, chaos synchronization is achieved in coupled chaotic oscillators, where the drive system variables control the response system. As a result, AS or LS or CS is demonstrated without using a variable delay line both experimentally and numerically.     

Phase synchronization in two coupled chaotic neurons

Chaotically-spiking dynamics of Hindmarsh–Rose neurons are discussed based on a flexible definition of phase for chaotic flow. The phase synchronization of two coupled chaotic neurons is in fact the spike synchronization. As a multiple time-scale model, the coupled HR neurons have quite different behaviors from the Rössler oscillators only having single time-scale mechanism. Using such a multiple time-scale model, the phase function can detect synchronization dynamics that cannot be distinguished by cross-correlation. Moreover, simulation results show that the Lyapunov exponents cannot be used as a definite criterion for the occurrence of chaotic phase synchronization for such a system. Evaluation of the phase function shows its utility in analyzing nonlinear neural systems.