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Bifurcations of periodic orbits in three-well Duffing system with a phase shift

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Abstract

Bifurcations of periodic orbits of three-well Duffing system with a phase shift are investigated in detail. The conditions of the existence and bifurcations for harmonics, subharmonics (2-order, 3-order and m-order) and superharmonics under small perturbations are given by using second-order averaging method and Melnikov’s method. The influence of the phase shift on the dynamics is also obtained.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, China

    Jicai Huang

  2. College of Information Technical Science, Nankai University, Tianjin, 300071, China

    Han Zhang

Authors
  1. Jicai Huang
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  2. Han Zhang
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Correspondence to Jicai Huang.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant No. 10726022, CCNU Project under Grant No. CCNU09A01003, and Tianjin Fund for Natural Sciences “07JCYBJC14700”.

This paper was recommended for publication by Editor Jinhu LÜ.

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Huang, J., Zhang, H. Bifurcations of periodic orbits in three-well Duffing system with a phase shift. J Syst Sci Complex 24, 519–531 (2011). https://doi.org/10.1007/s11424-010-8209-3

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  • DOI: https://doi.org/10.1007/s11424-010-8209-3

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