带有参数和外力激励的Josephson系统的复杂动态

Complex Dynamics in Josephson System with Parametric and External Excitations

摘要: 本文应用二阶平均方法和Melnikov理论，研究带有参数和外力激励的Josephson系统。给出了周期扰动下系统产生混沌的准则；得到了在拟周期扰动下当时平均系统的混沌存在准则；证明了当时，平均系统的混沌存在准则不能通过运用Melnikov方法给出；通过数值模拟验证了理论分析结果，并发现了系统的一些新的有趣的动态。

Abstract: In this paper, the Josephson system with parametric and external excitations by using second-order averaging methods and Melnikov’s methods is investigated in detail. The threshold values of existence of chaotic motion are obtained under the periodic perturbation. We prove the criterion of existence of chaos in averaged system under quasi-periodic perturbation for by applying the second-order averaging method and Melnikov’s method, and prove that the criterion of existence of chaos in second-order averaged system under quasi-periodic perturbation for cannot be obtained by applying Melnikov’s method. The theoretical results are verified and some new dynamics are demonstrated by numerical simulation.