Complex Dynamics in Josephson System with Parametric and External Excitations
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.
文章引用: 傅湘陵 , 陈晖荣 , 邓 进 (2013) 带有参数和外力激励的Josephson系统的复杂动态。 理论数学， 3， 149-168. doi: 10.12677/PM.2013.33024
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