Generalized Synchronization of Nonlinear Chaotic Systems through Natural Bioinspired Controlling Strategy

Abstract

A novel bioinspired control strategy design is proposed for generalized synchronization of nonlinear chaotic systems, combining the bioinspired stability theory, fuzzy modeling, and a novel, simple-form Lyapunov control function design of derived high efficient, heuristic and bioinspired controllers. Three main contributions are concluded: (1) apply the bioinspired stability theory to further analyze the stability of fuzzy error systems; the high performance of controllers has been shown in previous study by Li and Ge 2009, (2) a new Lyapunov control function based on bioinspired stability theory is designed to achieve synchronization without using traditional LMI method, which is a simple linear homogeneous function of states and the process of designing controller to synchronize two fuzzy chaotic systems becomes much simpler, and (3) three different situations of synchronization are proposed; classical master and slave Lorenz systems, slave Chen's system, and Rossler's system as functional system are illustrated to further show the effectiveness and feasibility of our novel strategy. The simulation results show that our novel control strategy can be applied to different and complicated control situations with high effectiveness.

Dynamic Analysis of Complex Synchronization Schemes between Integer Order and Fractional Order Chaotic Systems with Different Dimensions

“…Complete synchronization (CS), projective synchronization (PS), full state hybrid function projective synchronization (FSHFPS), and generalized synchronization (GS) are effective approaches to achieve synchronization and have been used widely in integer order chaotic systems [32][33][34][35] and fractional order chaotic systems [36][37][38][39]. Studying inverse problems of synchronization is an attractive and important idea.…”