新三维非线性混沌系统的动力学特性分析

Dynamical analysis of a new 3D nonlinear chaotic system

基于动力系统的理论和方法,结合理论分析和Matlab仿真,利用微分方程比较定理和多元函数的Lagrange乘数法,研究了一类新混沌系统的最终界和全局指数吸引集.对于系统的任意参数,分别得到了该混沌系统最终界和全局吸引集统一的数学表达式.最后,Matlab模拟验证了理论结果的正确性.为该系统的混沌控制、混沌同步、混沌吸引子维数的估计提供了理论依据.

Based on the theory and the method of dynamical systems,the authors further investigated complex dynamical behaviors of a new chaotic system by theoretical analysis and Matlab simulation combined method.The ultimate bounds and global attractive sets of the system were obtained.Then,the unified mathematical expression of the ultimate bounds and global attractive sets of the system were obtained by the comparison theorem of differential equations and Lagrange multiplier method.Finally,Matlab simulation result verified the correctness of the theoretical results.This article provides a theoretical basis for chaos control,chaos synchronization,chaos attractor dimension estimate of this system.