一类三维Jerk混沌系统的动力学分析

Dynamics Analysis of a 3D Jerk Chaotic System

针对一类三维Jerk混沌系统,运用数值理论分析该系统在不同参数条件下的周期1、周期2、混沌吸引子,以及Lyapunov指数谱和分叉等基本动力学行为。进而运用Poincare紧致化理论对系统的无穷远动力学进行分析,同时通过零倾线给出系统在无穷远点处的局部动力学行为。结果表明,该系统属于非Shilnikov型混沌系统,具有隐藏吸引子。

Basic dynamics such as period one attractor, period two attractor, chaotic attractor, Lyapunov exponent spectrum and bifurcation for a 3 D Jerk chaotic system are studied by using numerical methods. Also, by using the Poincare compactifi- cation of polynomial vector field, the dynamics near infinite singularities are obtained. Furthermore, the local phase portraits of the infinite singularities are obtained by using aclinic line. The simulation results demonstrate the system is a non - Shilnikov chaotic system and has a hidden attractor.