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Classification of homoclinic tangencies for periodically perturbed systems

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  • Tang, Yun
  • Yang, Fenghong
  • Chen, Guanrong
  • Zhou, Tianshou

Abstract

Classification of homoclinic tangencies for periodically perturbed systems is discussed. A relationship between the order of Melnikov function’s zeros and the harmonic components of a dynamical system is derived. By applying the singularity theory to the Melnikov function, possible types of homoclinic tangencies are studied for realization of the classification. In addition, certain multi-harmonically perturbed systems are investigated, showing the corresponding homoclinic bifurcation with their bifurcation diagrams.

Suggested Citation

  • Tang, Yun & Yang, Fenghong & Chen, Guanrong & Zhou, Tianshou, 2006. "Classification of homoclinic tangencies for periodically perturbed systems," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 76-89.
    • Handle: RePEc:eee:chsofr:v:28:y:2006:i:1:p:76-89
    DOI: 10.1016/j.chaos.2005.05.004
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    References listed on IDEAS

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    1. Yang, Xiaoli & Xu, Wei & Sun, Zhongkui & Fang, Tong, 2005. "Effect of bounded noise on chaotic motion of a triple-well potential system," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 415-424.
    2. Cao, Hongjun, 2005. "Primary resonant optimal control for homoclinic bifurcations in single-degree-of-freedom nonlinear oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1387-1398.
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