Discrete-time chaotic systems, impulsive synchronization and application in 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. 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. In this paper the concept of chaotic communication is based on digital chaotic systems where dual receivers are used for evaluation of information. The main advantage of digital chaotic systems is simple reproduction of devices, simple parameter setting and parameter stability. The dual receiver is used for improved function and error detection.