Discrete-Time Chaotic Systems Synchronization and Communication

A number of methods have been proposed for synchronizing chaotic systems. The most widely used methods are continuous synchronization schemes. In a continuous synchronization scheme, chaotic systems are coupled to each other continuously such that synchronization errors converge to zero. In this paper, chaos synchronization in coupled discrete time dynamical systems is presented. Especially, practical impulsive synchronization scheme for 3 discrete time chaotic systems is shown. Simulation results finally demonstrate the effectiveness of the method. Experimental results show that chaotic and hyperchaotic systems can be synchronized by impulses sampled from one or two state variables. The impulsive synchronization can be applied to almost all chaotic and hyperchaotic systems even in the case when continuous synchronization systems fail to work. The example of data transmission based on simple discrete-time chaotic systems is also presented.