Anticipating Synchronization And Lag Synchronization Of Chaotic Systems

In the last decade, synchronization of chaos has triggered considerable interest mainly because of a wide range of applications in physical, chemical and biological systems. Recently, much effort has been devoted to the theoretical analysis of anticipating synchronization after the observation of this kind of synchronization by Voss. However, synchronization of chaotic systems with parameter mismatches is rarely studied. In general, parameter mismatch is inevitable in the synchronization of practical chaotic systems due to noise or other artificial factors. It is relevant issue to investigate the effects of parameter mismatch on synchronization although there are only a few reports on this so far. In this dissertation, several criteria for the anticipating synchronization and lag synchronization of coupled chaotic systems are established. The main contributions of this dissertation are as follows:â‘ The anticipating synchronization of a class of coupled chaotic systems without-delay is studied. The asymptotic stability and exponential stability criteria for the involved error dynamical system are established by means of model transformation incorporated with Lyapunov-Krasovskii functional and linear matrix inequality. Based on the proposed stability conditions the coupling strength is then explicitly designed in terms of system parameters and anticipation time.â‘¡The anticipating synchronization of a class of coupled chaotic systems with parameter mismatches is studied. We estimate the error bound of anticipating synchronization by rigorously theoretical analysis.â‘¢The anticipating synchronization of a class of coupled chaotic systems with time delay and parameter mismatches is studied. The convergence criteria for the error dynamical system under study are established. The error bound of anticipating synchronization is estimated by rigorous theoretical analysis.â‘£The lag synchronization of a class of coupled chaotic systems with time delay and parameter mismatches is studied. Lag synchronization of coupled systems may weakly achieve in the presence of small parameter mismatches in terms of exponential stability criteria. The error bound of lag-synchronization arising from the parameter mismatches is also estimated by rigorously theoretical analysis.