Quasi-periodic excitation and dynamic stability for strained superlattice

Abstract

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.