Phase Synchronization Of Chaotic Oscillators Research Articles

Oscillations of Heart Rate and Respiration Synchronize During Affective Visual Stimulation

The objective of this study is to investigate the synchronization between breathing patterns and heart rate during emotional visual elicitation, that is, using sets of images gathered from the international affective picture system having five levels of arousal and five levels of valence, including a neutral reference level. Thirty-five healthy volunteers were emotionally elicited in agreement with a bidimensional spatial localization of affective states, i.e., arousal/valence plane, while two peripheral physiological signals, ECG and Respiration activity, were acquired simultaneously. The synchronization was then quantified by applying the concept of phase synchronization of chaotic oscillators, i.e., the cardio-respiratory synchrogram. This technique allowed us to estimate the synchronization ratio m:n as the attendance of n heartbeats in each m respiratory cycle, even for noisy and nonstationary data. We found a stronger evidence of cardiorespiratory synchronization during arousal than during neutral states.

Relationship between Phase Synchronization of Chaotic Oscillators and Time Scale Synchronization

The relationship between the phase synchronization of chaotic oscillators and their time scale synchronization has been considered, and it is established that the onset of the time scale synchronization depends on the resolving power of the base wavelet. This synchronization usually appears either before or (if said resolving power is insufficient) simultaneously with the onset of phase synchronization. The results are illustrated in the case of one-way coupled Rossler type dynamical systems.

Study on phase synchronization of chaotic oscillators with many rotational centers based on amplitude coupling

In order to find some relation between phase synchronization and dynamical topological variation in chaotic systems with many rotational centers,we propose a method of linear amplitude coupling to study the phase synchronization of Lorenz system and Duffing system.First,we convert the original Lorenz system and Duffing system into the dynamics of amplitude and phase.Based on linear amplitude coupling,we calculate the average winding number and Lyapunov exponents.We find that the phase synchronization comes along with the transition of Lyapunov exponents by increasing coupling strength.The results obtained indicate that phase synchronization is definitely related to dynamical topological variation in chaotic systems with many rotational centers.

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.

Phase Synchronization of Chaotic Rotators

We demonstrate the existence of phase synchronization of two chaotic rotators. Contrary to phase synchronization of chaotic oscillators, here the Lyapunov exponents corresponding to both phases remain positive even in the synchronous regime. Such frequency locked dynamics with different ratios of frequencies are studied for driven continuous-time rotators and for discrete circle maps. We show that this transition to phase synchronization occurs via a crisis transition to a band-structured attractor.

Noise scaling of phase synchronization of chaos

We investigate the effect of noise on phase synchronization of coupled chaotic oscillators. It is found that additive white noise can induce phase slips in integer multiples of 2p’s in parameter regimes where phase synchronization is observed in the absence of noise. The average time duration of the temporal phase synchronization scales with the noise amplitude in a way that can be described as superpersistent transient. We give two independent heuristic derivations that yield the same numerically observed scaling law. PACS number~s!: 05.45.Xt The phenomenon of synchronous chaos has attracted much attention since the work of Pecora and Carroll in 1990 @1#. Typically, when two chaotic oscillators are coupled together, synchronization between them can occur when the coupling strength is large enough. Recently, a more delicate type of synchronization phenomenon was discovered by Rosenblum, Pikovsky, and Kurths @2#. This is the phase synchronization of chaotic oscillators which occurs at smaller coupling strength than that required for complete synchronization. Briefly, if trajectories in each chaotic oscillator can be regarded as a rotation, then the phase angle of the rotation increases steadily with time: u(t)5vt1f(t), where v is the average rotation frequency and f(t) is a term characterizing chaotic fluctuations. As such, the rate of increase of phase can be modeled as a drift v plus a zero mean chaotic process. In the absence of coupling, the phase angles of the two oscillators u 1(t) and u 2(t) are uncorrelated. That is, if one measures the difference Du(t)[uu 1(t)2u 2(t)u, one finds that Du(t) increases steadily with time. However, when a small amount of coupling is present, Du(t) can be confined within 2p, while the amplitudes of the rotations are still completely uncorrelated. The bifurcation that leads to this phase synchronization was subsequently investigated @3‐5#. The ability of chaotic systems to have phase synchronization has implications on digital communication with chaos using the natural chaotic symbolic dynamics @6#. In such a case, it is highly desirable to suppress phase diffusions between chaotic communication channels to ensure proper timing for decoding. In this Brief Report, we address to what extent phase synchronization can be observed in laboratory experiments by investigating the effect of noise on phase synchronization. Our principal results are ~1! additive white noise, a type of noise encountered commonly in experimental situations, can induce phase slips in units of 2p between the coupled oscillators, which would otherwise be synchronized in phase in the absence of noise, and ~2! the average time duration between successive phase slips appears to obey a scaling law with the noise amplitude e,

Phase synchronization of chaotic oscillators by external driving

We extend the notion of phase locking to the case of chaotic oscillators. Different definitions of the phase are discussed. and the phase dynamics of a single self-sustanined chaotic oscillator subjected to external force is investigated. We describe regimes where the amplitude of the oscillator remains chaotic and the phase is synchronized by the external force. This effect is demonstrated for periodic and noisy driving. This phase synchronization is characterized via direct calculation of the phase, as well as by implicit indications, such as the resonant growth of the discrete component in the power spectrum and the appearance of a macroscopic average field in an ensemble of driven oscillators. The Rössler and the Lorenz systems are shown to provide examples of different phase coherence properties, with different response to the external force. A relation between the phase synchronization and the properties of the Lyapunov spectrum is discussed.

Phase synchronization in driven and coupled chaotic oscillators

We describe the effect of phase synchronization of chaotic oscillators. It is shown that phase can be defined for continuous time dynamical oscillators with chaotic dynamics, and effects of phase and frequency locking can be observed, We introduce several tools which characterize this weak synchronization and demonstrate phase and frequency locking by external periodic force, as well as due to weak interaction of nonidentical chaotic oscillators. In the synchronous state the phases of two systems are locked, while the amplitudes remain chaotic and noncorrelated. The intermittency phenomenon at the synchronization transition is considered. The application to the analysis of bivariate experimental data is discussed.