J. Nonl. Mod. Anal., 6 (2024), pp. 683-692.
Published online: 2024-08
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In this paper, a linear perturbation up to any order in $\epsilon$ for a cubic center with a multiple line of critical points is considered. By the algorithm of any order Melnikov function, the sharp upper bound of the number of limit cycles is 2.
}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2024.683}, url = {http://global-sci.org/intro/article_detail/jnma/23356.html} }In this paper, a linear perturbation up to any order in $\epsilon$ for a cubic center with a multiple line of critical points is considered. By the algorithm of any order Melnikov function, the sharp upper bound of the number of limit cycles is 2.