Research on the Expected Synchronization and Anticipating Synchronization of Time-delay Systems

It is a hard problem to anticipate the dynamic characteristics of non-linear chaotic system. In this paper, based on a stability theorem proved for linear chaotic systems, a scheme for anticipating synchronization of chaotic system is proposed. This paper investigate the synchronization between the receiver system and the future state of a transmitter system for an arbitrarily long anticipation time, both master and slave systems are considered to be involved with time-delay by the proposed method. The synchronization scheme guarantees one to predict the dynamics of chaotic transmitter at any point of time. Where synchronization error will be forced and then kept inside a ball around the origin. So the synchronization can be done with any desired accuracy. The proposed method can be easily extended to synchronize other chaotic systems. Numerical simulation results are used to verify the theoretical analysis using different values of parameter.