Subharmonic Bifurcations and Chaotic Dynamics for a Class of Ship Power System

Abstract

Subharmonic bifurcations and chaotic dynamics are investigated both analytically and numerically for a class of ship power system. Chaos arising from heteroclinic intersections is studied with the Melnikov method. The critical curves separating the chaotic and nonchaotic regions are obtained. The chaotic feature on the system parameters is discussed in detail. It is shown that there exist chaotic bands for this system. The conditions for subharmonic bifurcations with O type or R type are also obtained. It is proved that the system can be chaotically excited through finite subharmonic bifurcations with O type, and it also can be chaotically excited through infinite subharmonic bifurcations with R type. Some new dynamical phenomena are presented. Numerical simulations are given, which verify the analytical results.

The Application of Accurate Exponential Solution of a Differential Equation in Optimizing Stability Control of One Class of Chaotic System

“…The designed parameters of some nonlinear systems are diversified and the complicated application environment results in parameter fluctuation and uncertainty. Thus, it is necessary to control the chaotic system with unknown parameters [15]. This paper also gives an unknown parameter control process based on the above method, which not only makes the system's global exponent stable at the origin but also identifies unknown parameters according to the adaptation law of unknown parameters.…”