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Research Article | Open Access

Melnikov functions and limit cycle bifurcations for a class of piecewise Hamiltonian systems

Wenwen Hou, Maoan Han( )
School of Mathematical Sciences, Zhejiang Normal University, Jinhua, China
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Abstract

This study evaluated the number of limit cycles for a class of piecewise Hamiltonian systems with two zones separated by two semi-straight lines. First, we obtained explicit expressions of higher Melnikov functions. Then we applied these expressions to find the upper bounds of the number of limit cycles bifurcated from a period annulus of a piecewise polynomial Hamiltonian system.

Keywords

piecewise smooth systemMelnikov functionlimit cyclebifurcation
CLC number: 34C05, 34C07, 37G15

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AIMS Mathematics
Volume 9 Issue 2,
February 2024
Pages 3957-4013
DOI: 10.3934/math.2024194

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Cite this article:
Hou W, Han M. Melnikov functions and limit cycle bifurcations for a class of piecewise Hamiltonian systems. AIMS Mathematics, 2024, 9(2): 3957-4013. https://doi.org/10.3934/math.2024194

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Received: 14 November 2023
Revised: 22 December 2023
Accepted: 27 December 2023
Published: 15 February 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)