应变超晶格中粒子运动的混沌不稳定性

Chaos Instability of Particle Motion in Strained Superlattices

利用Fourier展开,将应变超晶格中的粒子运动问题转化为多频激励的摆方程问题。用Melnikov方法和Lyapunov方法讨论了系统的稳定性,并对双频激励和单频激励进行了具体分析。结果表明,多频激励系统可通过奇阶次谐分叉进入混沌;当阻尼系数比较大或激励强度比较弱时系统是稳定的。

The problem of particle motion in strained superlattices is transformed into a pendulum equation under multi-frequency excitation using Fourier expansion.The stability of the system is discussed with Melnikov method and Lyapunov method,and the dual frequency excitation and single frequency excitation are analyzed in detail.The results show that the multifrequency excitation system can enter the chaos via the odd-order subharmonic bifurcation,and the system is stable when the damping coefficient is relatively large or the excitation intensity is relatively weak.