# American Institute of Mathematical Sciences

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

## Bifurcations of periodic solutions and chaos in Josephson system

 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.
Citation: Zhujun Jing, K.Y. Chan, Dashun Xu, Hongjun Cao. Bifurcations of periodic solutions and chaos in Josephson system. Discrete and Continuous Dynamical Systems, 2001, 7 (3) : 573-592. doi: 10.3934/dcds.2001.7.573
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