Maximum number of limit cycles bifurcating from the period annulus of cubic polynomial systems

Shi, Hongwei; Bai, Yuzhen

doi:10.1090/proc/16096

Maximum number of limit cycles bifurcating from the period annulus of cubic polynomial systems
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by Hongwei Shi and Yuzhen Bai

Proc. Amer. Math. Soc. 151 (2023), 177-187

DOI: https://doi.org/10.1090/proc/16096

Published electronically: September 2, 2022

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Abstract:

This paper is devoted to the limit cycle bifurcation problem for some cubic polynomial systems, whose unperturbed systems have a period annulus and two invariant lines. Using the first order Melnikov function and Chebyshev criterion, we obtain the maximum number of limit cycles bifurcating from the period annulus. It improves a known result given by Sui and Zhao [Internat. J. Bifur. Chaos Appl. Sci. Engrg. 28 (2018), 1850063].

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