Chaotic Synchronization Via Minimum Information Transmission

Abstract

Chaotic synchronization is generally extremely sensitive to the presence of noise and other inference in the channel. Is this sensitivity a fundamental property of chaotic synchronization or is it related to the choice of synchronization method and can be suppressed by a modification of the method? If the answer is positive, then what are the relationships between the properties of a dynamical system and the level of noise at which the suppression of this sensitivity is still possible? What are particular methods to achieve synchronization that is stable to the presence of noise? In this paper we present the analysis of this issue from the standpoint of the information theory. The fundamental reason of this sensitivity is the fact that chaotic signal contains information and that requires a certain minimal threshold signal-to-noise ratio for this information to be transmitted. Only in this case high quality synchronization is achievable and only if the required information is transmitted (coded) optimally. Otherwise the threshold level can be much higher.