Noise-resistant chaotic synchronization of nonhyperbolic maps via information transmission

Abstract

Chaotic synchronization is generally extremely sensitive to the presence of noise and other interference in the channel. Is this sensitivity a fundamental property of chaotic synchronization or is it related to the choice of synchronization method and can it 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 stable to the presence of noise? In this paper we present the analysis of this issue from the standpoint of information theory. From this viewpoint the fundamental reason for this sensitivity is the fact that the chaotic signal contains information which requires a certain minimal threshold signal-to-noise ratio for transmission. Only in this case high-quality synchronization is transmitted (coded) optimally. Otherwise the threshold level can be much higher.