Coexisting Attractors in an Underwater Supercavitating Vehicle System

Abstract

Although supercavity can improve the speed of underwater vehicles greatly, the state of into water and parameters of system often lead vehicles move instability. This paper focuses on this problem. The existence of various coexisting attractors in this system is verified by distribution diagram of dynamic behaviors, and the motion of the vehicle varying with parameters and initial conditions is explored by basins of attraction. The results show that there are a few kinds of coexisting attractors at some parameter combinations of this system, such as two types of stable equilibrium points coexist with each other, a stable equilibrium point coexists with a limit cycle, a limit cycle coexists with a chaotic attractor and a 1-periodic cycle coexists with a 2-periodic cycle and so on, which explain the influence of parameters and initial values on the stability of vehicles qualitatively. In practical application, the stability of vehicles can be improved by setting parameters of system or adjusting initial launching conditions.