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

Yi Zhong and Yongqiang Fu

Journal of Mathematics, 2021, vol. 2021, 1-18

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.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:5140694

DOI: 10.1155/2021/5140694

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