Volume 5, Issue 1
Melnikov Functions for a Class of Piecewise Hamiltonian Systems

Wenwen Hou & Shanshan Liu

J. Nonl. Mod. Anal., 5 (2023), pp. 123-145.

Published online: 2023-08

[An open-access article; the PDF is free to any online user.]

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  • Abstract

This paper is concerned with the number of limit cycles for a class of piecewise Hamiltonian systems with two zones separated by two semistraight lines. By constructing a Poincaré map, we obtain explicit expressions of the first, second and third order Melnikov functions. In addition, we apply their expressions to give upper bounds of the number of limit cycles bifurcated from a period annulus of a piecewise polynomial Hamiltonian system.

  • AMS Subject Headings

34C05, 34C07, 37G15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-5-123, author = {Hou , Wenwen and Liu , Shanshan}, title = {Melnikov Functions for a Class of Piecewise Hamiltonian Systems}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2023}, volume = {5}, number = {1}, pages = {123--145}, abstract = {

This paper is concerned with the number of limit cycles for a class of piecewise Hamiltonian systems with two zones separated by two semistraight lines. By constructing a Poincaré map, we obtain explicit expressions of the first, second and third order Melnikov functions. In addition, we apply their expressions to give upper bounds of the number of limit cycles bifurcated from a period annulus of a piecewise polynomial Hamiltonian system.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2023.123}, url = {http://global-sci.org/intro/article_detail/jnma/21921.html} }
TY - JOUR T1 - Melnikov Functions for a Class of Piecewise Hamiltonian Systems AU - Hou , Wenwen AU - Liu , Shanshan JO - Journal of Nonlinear Modeling and Analysis VL - 1 SP - 123 EP - 145 PY - 2023 DA - 2023/08 SN - 5 DO - http://doi.org/10.12150/jnma.2023.123 UR - https://global-sci.org/intro/article_detail/jnma/21921.html KW - Piecewise smooth system, Melnikov function, Limit cycle, Bifurcation. AB -

This paper is concerned with the number of limit cycles for a class of piecewise Hamiltonian systems with two zones separated by two semistraight lines. By constructing a Poincaré map, we obtain explicit expressions of the first, second and third order Melnikov functions. In addition, we apply their expressions to give upper bounds of the number of limit cycles bifurcated from a period annulus of a piecewise polynomial Hamiltonian system.

Hou , Wenwen and Liu , Shanshan. (2023). Melnikov Functions for a Class of Piecewise Hamiltonian Systems. Journal of Nonlinear Modeling and Analysis. 5 (1). 123-145. doi:10.12150/jnma.2023.123
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