Phase synchronization of chaotic intermittent oscillations

We study phase synchronization effects of chaotic oscillators with a type-I intermittency behavior. The external and mutual locking of the average length of the laminar stage for coupled discrete and continuous in time systems is shown and the mechanism of this synchronization is explained. We demonstrate that this phenomenon can be described by using results of the parametric resonance theory and that this correspondence enables one to predict and derive all zones of synchronization.     

双频驱动混沌系统的相同步和广义同步

研究了双频混沌信号驱动的混沌振子的广义同步和相同步问题.发现了反偏向的相同步和正偏向的广义同步，即响应振子可以优先与驱动强度弱的混沌信号达到相同步，而广义同步则先在驱动强的信号和响应振子间建立起来.对这些行为产生的动力学机理进行了详细地分析. 关键词： 相同步 广义同步 条件熵 平均频率     

Phase synchronization in unidirectionally coupled chaotic ratchets

We study chaotic phase synchronization of unidirectionally coupled deterministic chaotic ratchets. The coupled ratchets were simulated in their chaotic states and perfect phase locking was observed as the coupling was gradually increased. We identified the region of phase synchronization for the ratchets and show that the transition to chaotic phase synchronization is via an interior crisis transition to strange attractor in the phase space.     

Phase synchronization in bi-directionally coupled chaotic ratchets

We show the existence of phase synchronization in bi-directionally coupled deterministic chaotic ratchets. The coupled ratchets were simulated in their chaotic states. A transition from a regime where the phases rotate with different velocities to a synchronous state where the phase difference is bounded was observed as the coupling was increased. In addition, the region of synchronization in which the system is permanently phase locked was identified. In this regime, the transverse Lyapunov exponent corresponding to both phases remain positive. Our calculations show that the transition to a synchronized state occurs via a crisis transition to an attractor filling the whole phase space.     

Phase synchronization in fractional differential chaotic systems

We propose an analytical justification for phase synchronization of fractional differential equations. This justification is based upon a linear stability criterion for fractional differential equations. We then investigate the existence of phase synchronization in chaotic forced Duffing and Sprott-L fractional differential systems of equations. Our numerical results agree with those analytical justifications.     

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.     

基于非线性观测器的一类混沌系统的相同步

研究了一类自治混沌系统的相同步问题.基于非线性状态观测器方法和极点配置技术，设计了相同步机理，并用该方法实现了一类自治混沌系统的相同步.通过对一种新的混沌系统的数值模拟，进一步验证了所提方案的有效性. 关键词： 混沌 相同步 非线性状态观测器 极点配置技术     

Regular and chaotic motion of coupled rotators

We consider a classical Hamiltonian H = L_z+M_z+L_xM_x, where the components of L and M satisfy Poisson brackets similar to those of angular momenta. There are three constants of motion: H, L² and M². By studying Poincaré surfaces of section, we find that the motion is regular when L² or M² is very small or very large. It is chaotic when both L² and M² have intermediate values. The interest of this model lies in its quantization, which involves finite matrices only.     

Phase synchronization of chaotic oscillations in terms of periodic orbits

We consider phase synchronization of chaotic continuous-time oscillator by periodic external force. Phase-locking regions are defined for unstable periodic cycles embedded in chaos, and synchronization is described in terms of these regions. A special flow construction is used to derive a simple discrete-time model of the phenomenon. It allows to describe quantitatively the intermittency at the transition to phase synchronization. (c) 1997 American Institute of Physics.     

Phase locking and chaotic synchronization in an array of three lasers

A linear array of three lasers that are coupled mutually in space is investigated. It is shown that the phase of the laser fields is locked with intermediate coupling while the laser intensities are totally chaotic and chaotically synchronized. When the intensities of lasers reenter the regime of chaotic synchronization at smaller coupling constant, the laser fields show low degree of phase locking. The phase differences in the fields between three lasers show rich patterns when the coupling is changed. Received 3 August 2001 and Received in final form 27 September 2001     

Stages of chaotic synchronization

In an experimental investigation of the response of a chaotic system to a chaotic driving force, we have observed synchronization of chaos of the response system in the forms of generalized synchronization, phase synchronization, and lag synchronization to the driving signal. In this paper we compare the features of these forms of synchronized chaos and study their relations and physical origins. We found that different forms of chaotic synchronization could be interpreted as different stages of nonlinear interaction between the coupled chaotic systems. (c) 1998 American Institute of Physics.     

Colored-noise-induced chaotic array synchronization

The effect of a time-correlated Gaussian noise on one-dimensional arrays consisting of diffusively coupled chaotic cells is analyzed. A resonance effect between the time scale of the chaotic attractor and the colored Gaussian noise has been found. As well, depending on the number of cells, coupling, and noise strength, an improvement of the synchronization or a poor synchronization between cells within the array can occur for some values of the time correlation. These nonlinear cooperative effects are studied in terms of a linear stability analysis around the uniform synchronized behavior.     

Impulsive synchronization of chaotic systems

The issue of impulsive synchronization of a class of chaotic systems is investigated. Based on the impulsive theory and linear matrix inequality technique, some less conservative and easily verified criteria for impulsive synchronization of chaotic systems are derived. The proposed method is applied to the original Chua oscillators, and the corresponding synchronization conditions are obtained. Moreover, the boundary of the stable region is also estimated in terms of the equidistant impulse interval. The effectiveness of our method is shown by computer simulation.     

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.     

Noise-induced phase synchronization and synchronization transitions in chaotic oscillators

Whether common noise can induce complete synchronization in chaotic systems has been a topic of great relevance and long-standing controversy. We first clarify the mechanism of this phenomenon and show that the existence of a significant contraction region, where nearby trajectories converge, plays a decisive role. Second, we demonstrate that, more generally, common noise can induce phase synchronization in nonidentical chaotic systems. Such a noise-induced synchronization and synchronization transitions are of special significance for understanding neuron encoding in neurobiology.     

Robust synchronization of uncertain chaotic systems

This paper investigates robust unified (lag, anticipated, and complete) synchronization of two coupled chaotic systems. By introducing the concepts of positive definite symmetrical matrix and Riccati inequality and the theory of robust stability, several criteria on robust synchronization are established. Extensive numerical simulations are also used to confirm the results.     

Impulsive generalized synchronization of chaotic system

In this paper, with a given manifold y= H(x) , we have constructed a response system for a continuous-time chaotic system as a drive system, and used impulsive control theory to demonstrate theoretically that this response system can achieve impulsive generalized synchronization (GS) with the drive system. Our theoretical result is supported by numerical examples.     

Experimental synchronization of single-transistor-based chaotic circuits

This work deals with nonautonomous chaotic circuits and, in particular, with the experimental characterization of the synchronization properties of two simple nonautonomous circuits. Two single-transistor chaotic circuits, which are among the simplest chaotic oscillators, are investigated. We studied synchronization of these circuits and found that the most appropriate technique to synchronize two single-transistor chaotic circuits is that based on the design of an inverse circuit.