A Design Method of Chaotic Synchronous Multi-stable Manifold

Abstract

Line spectra in the low frequency band of the underwater radiated noise are the main factors affecting the acoustic stealth performance of submarines. The chaotification technique for line spectra reduction can realize spectra reconstruction and reduce line spectra intensity by converting line spectra in the low frequency band into chaotic spectra in the broadband frequency. Previous studies have shown that the method of the generalized synchronization of chaos can generate continuous chaos of the system under variable operating conditions, and can reduce the amplitude significantly in some cases, which provides a new idea for the theory of the chaotification technique for line spectra reduction. However, this method can only select the appropriate synchronization control strategy of chaos through “trial and error” method to achieve chaos with small amplitude. Therefore, a design method of multiple stable synchronous manifolds including stable chaotic attractors with small amplitude is proposed. This method is verified and illustrated by the coupled Duffing system, and applied to the two degree-of-freedom (DOF) nonlinear vibration isolation system(VIS).