本文基于异宿轨道Shilnikov定理,研究了一类分段线性混沌系统的构造方法.这类混沌系统含有两个或两个以上平衡点,且在各个平衡点处具有相同的雅戈比矩阵.通过改变系统平衡点和转换平面的个数及相对位置,得到了这类混沌系统的若干形式.进一步地,将三维系统的构造推广到高维系统,又得到了四维混沌系统的若干形式.最后给出了具体的实现电路.

The construction of a kind of piecewise linear chaotic system is investigated based on the heteroclinic shilnikov theorem.These systems have at least two equilibriums and at each equilibrium they have the same Jacobian matrix.According to the amount of the equilibriums and the relative positions of the separating planes,some different chaotic systems of this kind can be obtained.Furthermore,the proposed method is extended to the construction of the higher dimensional systems,and some 4-D chaotic systems are also obtained.Finally,the circuit implementation of the system is given.