镜像变换原理及其在非线性动力系统中的应用

摘要

This paper further investigates the principle and mathematical proof of mirror conversion and its application on nonlinear dynamical systems, and generates two kinds of grid attractor dynamical systems.First, by mirror symmetry conversion in z direction, 2×2-wing chaotic attractor is obtained from a three-dimensional chaotic system.Second, by the mirror symmetry conversion with respect to u-axis, intended grid 2×2-wing hyperchaotic attractor can be obtained.This paper provides the numerical simulation results of the two kinds of grid attractor, which has demonstrated the feasibility of the proposed approaches.%给出镜像变换原理并对其进行数学证明,将此原理运用到非线性动力系统中,产生两类网格多翅膀吸引子动力系统.首先基于一个混沌系统,对该混沌系统做关于z轴的镜像对称变换,得到一个2×2翅膀的混沌系统.其次基于一个超混沌系统,对该超混沌系统做关于u轴的镜像对称变换,得到一个2×2翅膀超混沌系统.文中给出两类网格多翅膀吸引子动力系统的仿真结果,证实该原理的可行性.