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

Wenwen Hou; Maoan Han; Wenwen Hou; Maoan Han

doi:10.3934/math.2024194

AIMS Mathematics

2024, Volume 9, Issue 2: 3957-4013. doi: 10.3934/math.2024194

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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

Received: 14 November 2023 Revised: 22 December 2023 Accepted: 27 December 2023 Published: 11 January 2024
MSC : 34C05, 34C07, 37G15

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.
- piecewise smooth system,
- Melnikov function,
- limit cycle,
- bifurcation
Citation: Wenwen Hou, Maoan Han. Melnikov functions and limit cycle bifurcations for a class of piecewise Hamiltonian systems[J]. AIMS Mathematics, 2024, 9(2): 3957-4013. doi: 10.3934/math.2024194

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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.

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