准周期激励与应变超晶格的动力学稳定性

假设超晶格锯齿形沟道对粒子的作用等效为形状相似的周期场作用. 在经典力学框架内，引入正弦平方势，把粒子运动方程化为具有阻尼项和双频激励项的摆方程. 用Melnikov方法对单频激励系统的分叉与混沌进行分析；用Lyapunov方法对双频激励系统的稳定性进行讨论. 结果表明：在弱非线性情况下，双频激励系统存在局域不稳定，且这种不稳定将向全局扩展，直至混沌的出现；导致混沌的双频激励强度远小于单频激励强度；外加一个适当的超声场可望将这种敏感钝化，使系统的稳定性得到改善. 关键词： 超晶格 准周期激励 混沌 稳定性

Quasi-periodic excitation and dynamic stability for strained superlattice

In this paper, the action exerted by a superlattice sawtooth-shaped channel on the particle is assumed to be equivalent to that exerted by a periodic field with a similar shape. In the framework of classical mechanics, by introducing the sines-quared potential, the particle motion equation is reduced to pendulum equation with a damping term and dual-frequency excitation term. The bifurcation and chaos of single-frequency excitation system are analyzed with the Melnikov method. The stability of dual-frequency excitation system is discussed by using the Lyapunov exponent. The results show that in the case of weak nonlinearity, local instability can be found in the dual frequency excitation system, and it will be expanded globally until chaos appears. The dual excitation intensity leading to chaos is far less than that of single-frequency excitation. The application of an appropriate ultrasonic field is likely to make such a sensitivity passivated, and the stability of the system improved as well.
Keywords： superlattice quasi-periodic excitation chaos stabilities