Three Types of Transitions to Phase Synchronization in Coupled Chaotic Oscillators (original) (raw)

Phase synchronization of chaotic oscillators

Physical Review Letters, 1996

We present the new effect of phase synchronization of weakly coupled self-sustained chaotic oscillators. To characterize this phenomenon, we use the analytic signal approach based on the Hilbert transform and partial Poincaré maps. For coupled Rössler attractors, in the synchronous regime the phases are locked, while the amplitudes vary chaotically and are practically uncorrelated. Coupling a chaotic oscillator with a hyperchaotic one, we observe another new type of synchronization, where the frequencies are entrained, while the phase difference is unbounded. A relation between the phase synchronization and the properties of the Lyapunov spectrum is studied.

Phase synchronization in driven and coupled chaotic oscillators

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 1997

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.

Oscillatory and rotatory synchronization of chaotic autonomous phase systems

Physical review. E, Statistical, nonlinear, and soft matter physics, 2003

The existence of rotatory, oscillatory, and oscillatory-rotatory synchronization of two coupled chaotic phase systems is demonstrated in the paper. We find four types of transition to phase synchronization depending on coherence properties of motions, characterized by phase variable diffusion. When diffusion is small the onset of phase synchronization is accompanied by a change in the Lyapunov spectrum; one of the zero Lyapunov exponents becomes negative shortly before this onset. If the diffusion of the phase variable is strong then phase synchronization and generalized synchronization, occur simultaneously, i.e., one of the positive Lyapunov exponents becomes negative, or generalized synchronization even sets in before phase synchronization. For intermediate diffusion the phase synchronization appears via interior crisis of the hyperchaotic set. Soft and hard transitions to phase synchronization are discussed.

From phase to lag synchronization in coupled chaotic oscillators

Physical Review Letters, 1997

We study synchronization transitions in a system of two coupled self-sustained chaotic oscillators. We demonstrate that with the increase of coupling strength the system first undergoes the transition to phase synchronization. With a further increase of coupling, a new synchronous regime is observed, where the states of two oscillators are nearly identical, but one system lags in time to the other. We describe this regime as a state with correlated amplitudes and a constant phase shift. These transitions are traced in the Lyapunov spectrum. [S0031-9007(97)03271-7] PACS numbers: 05.45.+b

Synchronization of coupled chaotic oscillators as a phase transition

2005

We characterize the synchronization of an array of coupled chaotic elements as a phase transition where order parameters related to the joint probability at two sites obey power laws versus the mutual coupling strength; the phase transition corresponds to a change in the exponent of the power law. Since these studies are motivated by the behaviour of the cortical neurons

Phase Synchronization in Regular and Chaotic Systems

International Journal of Bifurcation and Chaos, 2000

In this contribution we present a brief introduction to the theory of synchronization of selfsustained oscillators. Classical results for synchronization of periodic motions and effects of noise on this process are reviewed and compared with recently found phase synchronization phenomena in chaotic oscillators. The basic notions of phase and frequency locking are reconsidered within a common framework. The application of phase synchronization to data analysis is discussed.

Phase synchronization between two essentially different chaotic systems

Physical Review E, 2005

In this paper, we numerically investigate phase synchronization between two coupled essentially different chaotic oscillators in drive-response configuration. It is shown that phase synchronization can be observed between two coupled systems despite the difference and the large frequency detuning between them. Moreover, the relation between phase synchronization and generalized synchronization is compared with that in coupled parametrically different systems. In the systems studied, it is found that phase synchronization occurs after generalized synchronization in coupled essentially different chaotic systems.

Role of unstable periodic orbits in phase and lag synchronization between coupled chaotic oscillators

Chaos, 2003

An increase of the coupling strength in the system of two coupled Rössler oscillators leads from a nonsynchronized state through phase synchronization to the regime of lag synchronization. The role of unstable periodic orbits in these transitions is investigated. Changes in the structure of attracting sets are discussed. We demonstrate that the onset of phase synchronization is related to phase-lockings

Two scenarios of breaking chaotic phase synchronization

Technical Physics, 2007

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.

Synchronization of mutually coupled chaotic systems

Physical Review E, 1997

We report on the experimental observation of both basic frequency locking synchronization and chaos synchronization between two mutually coupled chaotic subsystems. We show that these two kinds of synchronization are two stages of interaction between coupled chaotic systems. In particular the chaos synchronization could be understood as a state of phase locking between coupled chaotic oscillations.