Bifurcations of periodic solutions and chaos in Josephson system

Zhujun Jing; K.Y. Chan; Dashun Xu; Hongjun Cao

doi:10.3934/dcds.2001.7.573

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2001, Volume 7, Issue 3: 573-592. Doi: 10.3934/dcds.2001.7.573

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Bifurcations of periodic solutions and chaos in Josephson system

1.
Dept. of Math., Hunan Normal University, Hunan Changsha
2.
Department of Mathematics University of Hong Kong
3.
Inst. of Math., Chinese Academy of Sciences, Beijing 100080

Received: May 31, 2000

Revised: November 30, 2000

Published: June 2001

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Abstract

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:

Josephson systems,
bifurcations,
periodic solution,
chaos,
second-order averaging and Melnikov methods.

Mathematics Subject Classification: 34C32, 35B32.

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