不连续不可逆二维映象的动力学特性

Dynamical properties of discontinuous and noninvertible two-dimensional map

总结两个保守映象不可逆地分段连续链接(称为类耗散系统)以及一个保守映象与一个耗散映象不可逆地分段连续链接(称为半耗散系统)情况下得到的五项共同动力学特征:不连续边界象集构成的随机网成为唯一的混沌轨道;由于某些相点具有两个逆象而导致的相空间塌缩(类耗散);由于系统的不连续不可逆性质而出现的胖分形禁区网;在具有吸引子共存时占据不连续边界象集随机网和胖分形禁区网区域的点滴状吸引域以及由此导致的吸引子不可预言性;即使在传统强耗散存在的情况下点滴状吸引域仍由类耗散机制主宰.以一个累积触发电路为例,说明这五项系统动力学共性在两个耗散映象不可逆地分段连续链接的情况下仍存在,因此它们是不连续不可逆二维映象的动力学共性.

This paper reports five different features in piecewise continuous and noninvertible system described by two conservative maps or one conservative map and another dissipative map. The features are as follows ： the stochastic web bounded by images of discontinuous borderline is the only chaotic trajectory; phase collapse is caused by the irreversibility which makes some points to have two pre-images ; fat fractal forbidden web induced by irreversibility; riddled-like attraction basin in stochastic web and forbidden web, when there are different attractors coexisting; and the impossibility to tell to which attractor an initial condition will approach. In an integrate-and-fire circuit, we find that the features still exist in the circuit system described by two dissipative maps, so they are common features in discontinuous and noninvertible maps.