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A High-Order Melnikov Method for Heteroclinic Orbits in Planar Vector Fields and Heteroclinic Persisting Perturbations

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  • Yi Zhong
  • Yongqiang Fu

Abstract

This work extends the high-order Melnikov method established by FJ Chen and QD Wang to heteroclinic orbits, and it is used to prove, under a certain class of perturbations, the heteroclinic orbit in a planar vector field that remains unbroken. Perturbations which have this property together form the heteroclinic persisting space. The Van der Pol system is analysed as an application.

Suggested Citation

  • Yi Zhong & Yongqiang Fu, 2021. "A High-Order Melnikov Method for Heteroclinic Orbits in Planar Vector Fields and Heteroclinic Persisting Perturbations," Journal of Mathematics, Hindawi, vol. 2021, pages 1-18, December.
    • Handle: RePEc:hin:jjmath:5140694
    DOI: 10.1155/2021/5140694
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