Study on general criteria for generalized chaotic synchronization with a desired manifold

Abstract

One of the techniques to improve the underwater acoustic stealth performance of ships is to use the wide-spectrum characteristics of chaotic signals to weaken the line spectrum of radiated underwater acoustic signals. To modulate the signal in an expected way, this paper proposes a criterion for constructing a bidirectionally coupled system based on the original system, which enables the response system and the drive system to achieve generalized chaotic synchronization with the desired manifold and gives a method to determine the reliable interval of coupling coefficients. The simplified criterion is suitable for constructing a unidirectionally coupled system. Taking the Chen system and Chua’s circuit as examples, the reliable interval of coupling coefficient is deduced by using the proposed criterion. Bidirectionally coupled chaotic systems are constructed for the desired linear manifold and nonlinear manifold, and the validity of the construction method and the criterion is verified by numerical simulation.