Suochun Zhang

Chaos synchronization between linearly coupled chaotic systems

This paper investigates the chaos synchronization between two linearly coupled chaotic systems. Some sufficient conditions of global asymptotic synchronization are attained from rigorously mathematical theory. Also, a new method for analyzing the stability of synchronization solution is presented. Using this method, some sufficient conditions of linear stability of the synchronization chaotic solution are gained. The influence of coupling coefficients on chaos synchronization is further studied for three typical chaotic systems: Lorenz system, Chen system, and newly found L€ system. 2002 Elsevier Science Ltd. All rights reserved.

Dynamical analysis of a new chaotic attractor

Dynamical behaviors of a new chaotic attractor is investigated in this paper. Some basic properties, bifurcations, routes to chaos, and periodic windows of the new system are studied either analytically or numerically. Meanwhile, the transition between the Lorenz attractor and Chens attractor through the new system is explored.

The compound structure of a new chaotic attractor

Abstract This paper reports the finding of the compound structure of a new chaotic attractor, which is obtained by merging together two simple attractors after performing a mirror operation. Furthermore, the forming mechanism of the new chaotic attractor is investigated.

LOCAL BIFURCATIONS OF THE CHEN SYSTEM

This paper introduces a new practical method for distinguishing chaotic, periodic and quasi-periodic orbits based on a new criterion, and apply it to investigate the local bifurcations of the Chen system. Conditions for supercritical and subcritical bifurcations are obtained, with their parameter domains specified. The analytic results are also verified by numerical simulation studies.

Hopf bifurcation in the Lü system

Abstract In this paper, we use a novel method to investigate the stability of Lu system. It is shown that the Lu system will display a Hopf bifurcation under certain conditions. Finally, we obtain the conditions of supercritical and subcritical bifurcation.

THE COMPOUND STRUCTURE OF CHEN'S ATTRACTOR

This Letter reports the finding of the compound structure of Chens attractor, which is obtained by merging together two simple attractors after performing a mirror operation. Also, the forming procedure of Chens attractor is explored.

Generating two simultaneously chaotic attractors with a switching piecewise-linear controller

It has been demonstrated that a piecewise-linear system can generate chaos under suitable conditions. This paper proposes a novel method for simultaneously creating two symmetrical chaotic attractor––an upper-attractor and a lower-attractor––in a 3D linear autonomous system. Basically dynamical behaviors of this new chaotic system are further investigated. Especially, the chaos formation mechanism is explored by analyzing the structure of fixed points and the system trajectories.

CONTROLLING IN BETWEEN THE LORENZ AND THE CHEN SYSTEMS

This letter investigates a new chaotic system and its role as a joint function between two complex chaotic systems, the Lorenz and the Chen systems, using a simple variable constant controller. With the gradual tuning of the controller, the controlled system evolves from the canonical Lorenz attractor to the Chen attractor through the new transition chaotic attractor. This evolving procedure reveals the forming mechanisms of all similar and closely related chaotic systems, and demonstrates that a simple control technique can be very useful in generating and analyzing some complex chaotic dynamical phenomena.

A new proof for existence of horseshoe in the Rossler system

Abstract A new simple computer-assisted proof based on a newly established topological horseshoe theorem is given for the existence of horseshoe in the well known Rossler system.

Echo waves and coexisting phenomena in coupled brusselators

Abstract In this paper we study the echo wave and coexisting phenomena in linearly coupled brusselators and put forward a new method to prove the existence of the echo wave. We find that the existence of the echo wave is determined by that of the periodic solution of the associate oscillator. In addition, we also find that the stable steady state may coexist with the echo wave and that the echo wave may coexist with the in-phase wave under suitable conditions, and specify the coexisting regimes on parameters.