不可微不可逆映象中的V型阵发

TYPE V INTERMITTENCY IN NONDIFFERENTIABLE AND NONINVERTIBLE MAPS

一个既不可微(或不连续)又不可逆的一维映象可以展示一种新型的阵发。它的机制是稳定不动点与映象不可微或不连续点碰撞而消失。这种阵发可以在该不动点附近的线性化映象本征值绝对值在阵发前为小于1的任何值的情况发生,因而可能突然出现在倍周期分岔序列中途任一部分,使序列中断进入混沌。在稳定不动点消失后映象产生的阵发时间序列中,层流相长度呈现与外控参数距临界值距离的对数依赖关系。这种新型标度规律不依赖于映象的细节。作者认为这种阵发应广泛存在于许多实际系统之中。

A both nondifferentiable (or discontinuous ) and noninvertible one-dimensional map can display a new type of intermittency. The mechanism of it is that a stable fixed point collides with the nondifferentiable of discontinuous point of the map and then disappears. This type of intermittency can happen in the case when the absolute eigenvalue of the linearised map near the fixed point equals any number smaller than 1 before the intermittency. Therefore, it can appear suddenly in any part between a period-doubling cascade, interrupt the cascade and lead to chaos. In the intermittent time plot after disappearence of the stable fixed point the dura-tion of the laminar phase follows a logarithmic dependence on the distance between a control parameter value and its critical number. This new scaling law is independent of the details of the map. We believe that this new type of intermittency should exist in many practical sys-tems.