一类不可逆保守系统中的混沌类吸引子

A chaotic quasi-attractor in a kind of noninvertible conservative systems

报道一类不可逆保守系统的性质及在其中发现的混沌类吸引子 .这些系统可以看作是一种加过压保护的张弛振荡电路的简化模型 .它展示的类吸引性是指这个混沌轨道吸引它之外的迭代 ,而这种吸引由系统的不可逆性所导致 .数值研究发现这个混沌轨道就是系统不连续边界的映象集 ,而且这很可能是这类系统的普遍性质 .

This paper reports a chaotic quasi-attractor discovered in a kind of noninvertible conservative systems. The systems can be viewed as simplified models for an electronic relaxation oscillator with voltage protection. The quasi-attracting property displayed by them denotes that some chaotic trajectories attract iterations outside them, and that the attraction is induced by the noninvertibility of the system. Our numerical studies indicate that the chaotic trajectories are formed by the set of images of the discontinuous border of the system. This behaviour very likely is a common property of this kind of systems.