Construction of Chaotically Synchronizing Systems and Some Methods of Controlling Chaos

Perhaps the most well known of the propert ies that characterize chaotic systems is their sensitivity to initial conditions. Two identical chaotic systems that are started from virtually identical initial condi t ions in a short time would be observed to diverge f rom one another . However, for chaotic systems one observes a very impor tan t phenomenon called chaot ic synchronization. This is a nonlinear phenomenon such that the behaviors of a subsystem are chaot ic but take the same values as those in another subsystem. Pecora and Caroll [1] proposed a method for synthesizing a nonlinear system with chaotic synchronizat ion in a so called master-slave configuration. The P C method is very simple and applied to many chaot ic systems [2, 3]. Chaot ic synchronizat ion is a very useful phenomenon in engineering and many secure communi cat ion methods using it are proposed [4, 5]. There, an information signal containing a message is t ransmitted using a chaotic signal as a b r o a d b a n d carrier, and the synchronization is necessary to recover the informat ion at the receiver. For example in [6, 7] the informat ion signal is added to the chaot ic signal and in [5] a parametr ic modula t ion is used for the t ransmission of digital signals.