多重魔梯的一个数值例证

An Numerical Evidence of Multiple Devil's Staircase

关键词:  对称多重魔梯  碰撞模式  不连续系统

Key words:  symmetric multiple Devil's staircase  collision mode  discontinous system

摘要:

介绍在电子张弛振子中观察到的对称多重魔梯,它实际只有两个不连续点,但所谓的特征周期点随参数变化的移动方向在其中的一个锁相台阶内发生了改变,由此导致3个碰撞模式,其中2个完全对称.在此基础上,构造和解析多重魔梯的简化模型,结果说明映象函数斜率的非线性变化能够导致类似的现象.

Abstract:

An occurrence of a symmetric multiple Devil's staircase in an electronic relaxation oscillator was reported.In this system,there actually are two discontinuous points.However,the changing of moving direction of the so-called characteristic periodic point inside one of the phase-locked plateaus lead to three modes.Two of them are exactly symmetric.A simplified model to show that a nonlinear variation of mapping function slope can induce this phenomenon were constructed.