American Institute of Mathematical Sciences

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July  2001, 7(3): 573-592. doi: 10.3934/dcds.2001.7.573

Bifurcations of periodic solutions and chaos in Josephson system

Zhujun Jing 1, , K.Y. Chan 2, , Dashun Xu 3, and  Hongjun Cao 3,

1. 

Dept. of Math., Hunan Normal University, Hunan Changsha, China
2. 

Department of Mathematics University of Hong Kong, China
3. 

Inst. of Math., Chinese Academy of Sciences, Beijing 100080, China, China

Received  June 2000 Revised  December 2000 Published  April 2001

The Josephson equation is investigated in detail: the existence and bifurcations for harmonic and subharmonic solutions under small perturbations are obtained by using second-order averaging method and subharmonic Melnikov function, and the criterion of existence for chaos is proved by Melnikov analysis; the bifurcation curves about n-subharmonic and heteroclinic orbits and the driving frequency $\omega$ effects to the forms of chaotic behaviors are given by numerical simulations.
Keywords: second-order averaging and Melnikov methods., bifurcations, chaos, periodic solution, Josephson systems.
Mathematics Subject Classification: 34C32, 35B3.
Citation: Zhujun Jing, K.Y. Chan, Dashun Xu, Hongjun Cao. Bifurcations of periodic solutions and chaos in Josephson system. Discrete & Continuous Dynamical Systems - A, 2001, 7 (3) : 573-592. doi: 10.3934/dcds.2001.7.573
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