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.

The chaotification method can be used to weaken the line spectra component of the ship's radiated noise. The main obstacle that plagues the engineering realization of this innovative concept is how to realize the small-amplitude chaotic motion of the nonlinear vibration isolation system (NVIS) in a large parameter range and how to maintain the chaotic state under variable operating conditions. In this paper, the dimensionless dynamic equation of the NVIS with a flexible base is derived. A control method similar to generalized synchronization is used to realize the continuous chaos of the system. The maximum Lyapunov exponent, the conditional Lyapunov exponent, and disturbances are introduced to verify the effectiveness of the control method and its stability and robustness in a large range of parameters. Aiming at the coexistence of multiple attractors, a new global analysis method is proposed, which is used to study the distribution of basin of attraction (BA). According to the changes of BA before and after the system is controlled, the BA is partitioned. Initial conditions from different partitions are selected to study the attenuation effect of line spectra and vibration, and the favorable initial conditions for realizing the small-amplitude chaotic motion of the system are given. The method may be extended to the global analysis of other controlled systems.

In this paper, a general criterion for unidirectionally coupled generalized chaotic synchronization between the response system and the original chaotic system in the form of a desired manifold is presented. The expression of the response system constructed with linear error feedback is given, and the validity of the criterion is proved based on the Lyapunov stability theory. Two numerical examples are used to construct unidirectional coupled chaotic systems in the form of different types of manifolds. Numerical simulation is carried out to verify the feasibility of the construction method and the criterion.