一类新的边界激变现象:混沌的边界激变

混沌吸引子的激变是一类普遍现象.借助于广义胞映射图论(generalized cell mapping digraph)方法发现了嵌入在分形吸引域边界内的混沌鞍,这个混沌鞍由于碰撞混沌吸引子导致混沌吸引子完全突然消失,是一类新的边界激变现象,称为混沌的边界激变.可以证明混沌的边界激变是由于混沌吸引子与分形吸引域边界上的混沌鞍相碰撞产生的,在这种情况下,当系统参数通过激变临界值时,混沌吸引子连同它的吸引域突然消失,同时这个混沌鞍也突然增大 关键词： 广义胞映射 有向图 激变 混沌鞍

A NEW TYPE OF BOUNDARY CRISES: CHAOTIC BOUNDARY CRISES

Crises of chaotic attractors are typical phenomena in nonlinear dynamical systems. By means of generalized cell mapping digraph (GCMD) method, we show that a chaotic boundary crisis results from a collision between a chaotic attractor and a chaotic saddle in the fractal basin boundary. In such a case the chaotic attractor, together with its basin of attraction, is suddenly destroyed as the parameter passes through a critical value, simultaneously the chaotic saddle also undergoes an abrupt enlargement in its size.