Melnikov analysis in a cubic system with a multiple line of critical points

In this paper, the first fourth order Melnikov analyses are applied to find the limit cycles bifurcated from a cubic center under the perturbation of quadratic polynomials in ϵ up to the second order. The upper bounds of the number of limit cycles are given and can be reached.

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Bibliographic Details
Published in:Applied mathematics letters 2023-11, Vol.145, p.108787, Article 108787
Main Authors: Yang, Peixing, Yu, Jiang
Format: Article
Language:English
Subjects:
Bifurcation
Limit cycles
Melnikov functions
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Summary:In this paper, the first fourth order Melnikov analyses are applied to find the limit cycles bifurcated from a cubic center under the perturbation of quadratic polynomials in ϵ up to the second order. The upper bounds of the number of limit cycles are given and can be reached.
ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2023.108787