Generalized Synchronization of Time-Delayed Discrete Systems

This paper establishes two theorems for two time-delayed （chaotic） discrete systems to achieve timedelayed generalized synchronization （TDGS）. These two theorems uncover the genera/forms of two TDGS systems via a prescribed transformation. As examples, we convert the Lorenz three-dimensional chaotic map to an equal time-delayed system as the driving system, and construct the TDGS driven systems according to the Theorems 1 and 2. Numerical simulations demonstrate the effectiveness of the proposed theorems.     

Generalized Synchronization of Time-Delayed Differential Systems

We establish two theorems for two time-delayed （chaotic） differential equation systems to achieve time-delayed generalized synchronization （TDGS）. The theorems uncover general forms of two TDGS systems via a prescribed differentiable transformation. Based on the theorems, we use two-coupled Ikeda equations as the driving system to construct TDGS driven systems via two prescribed transformations. Numerical simulations demonstrate the effectiveness of the proposed theorems. It may be expected that our theorems provide new tools for understanding and studying TDGS phenomena.     

Adaptive generalized projective synchronization of two different chaotic systems with unknown parameters

This paper presents a general method of the generalized projective synchronization and the parameter identification between two different chaotic systems with unknown parameters. This approach is based on Lyapunov stability theory, and employs a combination of feedback control and adaptive control. With this method one can achieve the generalized projective synchronization and realize the parameter identifications between almost all chaotic （hyperchaotic） systems with unknown parameters. Numerical simulations results are presented to demonstrate the effectiveness of the method.     

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.     

Theory and Applications of Discontinuous State Feedback Generating Chaos for Linear Systems

We investigate a kind of chaos generating technique on a type of n-dimensional linear differential systems by adding feedback control items under a discontinuous state. This method is checked with some examples of numeric simulation. A constructive theorem is proposed for generalized synchronization related to the above chaotic system.     

Generalized projective synchronization of a class of chaotic （hyperchaotic） systems with uncertain parameters

In this paper is investigated the generalized projective synchronization of a class of chaotic （or hyperchaotic） systems, in which certain parameters can be separated from uncertain parameters. Based on the adaptive technique, the globally generalized projective synchronization of two identical chaotic （hyperchaotic） systems is achieved by designing a novel nonlinear controller. Furthermore, the parameter identification is realized simultaneously. A sufficient condition for the globally projective synchronization is obtained. Finally, by taking the hyperchaotic L system as example, some numerical simulations are provided to demonstrate the effectiveness and feasibility of the proposed technique.     

Adaptive generalized functional synchronization of chaotic systems with unknown parameters

A universal adaptive generalized functional synchronization approach to any two different or identical chaotic systems with unknown parameters is proposed, based on a unified mathematical expression of a large class of chaotic system. Self-adaptive parameter law and control law are given in the form of a theorem. The synchronization between the three-dimensional R6ssler chaotic system and the four-dimensional Chen＇s hyper-chaotic system is studied as an example for illustration. The computer simulation results demonstrate the feasibility of the method proposed.     

Impulsive Synchronization of Discrete Chaotic Systems

Impulsive synchronization of two chaotic maps is reformulated as impulsive control of the synchronization error system.We then present a theorem on the asymptotic synchronization of two chaotic maps by using synchronization impulses with varying impulsive intervals,As an example and application of the theroem,we derives some sufficient conditions for the synchronization of two chaotic Lozi maps via impulsive control.The effectivness of this approach has been demonstrated with chaotic Lozi map.     

Generalized synchronization of two different chaotic systems

In this paper, generalized synchronization of two different chaotic dynamical systems is investigated. An active control is adopted to construct a response system which synchronizes with a given drive system for a function relation. Based on rigorous analysis, the error system is asymptotically stable at the equilibrium. Numerical simulations illustrate the effectiveness of the proposed theory.     

Comparison of Phase Synchronizability of Several Regular Networks for Non-Phase-Coherent Attractors

Though applying master stability function method to analyse network complete synchronization has been well studied in chaotic dynamical systems, it does not work well for phase synchronization. Moreover, it is difficult to identify phase synchronization with the angle of rotation for non-phase-coherent attractors. We employ the recurrences plot method to detect phase synchronization for several regular networks with non-phase-coherent attractors. It is found that the coupling strength μ is different for different coupled networks. The coupling strength μ is reduced as completed coupled network scale enlarges, the coupling strength μ of star coupled network is irrelevant to network scale, and these two regular networks are easier to achieve phase synchronization. However, for ring and chain coupled networks, the larger the phase synchronization couple strength μ is, the larger the network scale is, and it is more difficult to achieve phase synchronization. For same scale network, once ring coupled structure becomes a chain coupled structure, phase synchronization becomes much more difficult.