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Volume 4, Issue 2
The Number of Limit Cycles in a Class of Piecewise Polynomial Systems

Shanshan Liu, Xuyi Jin & Yujie Xiong

DOI: 10.12150/jnma.2022.352

J. Nonl. Mod. Anal., 4 (2022), pp. 352-370.

Published online: 2022-06

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

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  • Abstract

In this paper, we pay attention to the number of limit cycles for a class of piecewise smooth near-Hamiltonian systems. By using the expression of the first order Melnikov function and some known results about Chebyshev systems, we study upper bound of the number of limit cycles in Hopf bifurcation and Poincaré bifurcation respectively.

  • Keywords

Piecewise smooth system, Melnikov function, ECT-system, Limit cycle.

  • AMS Subject Headings

37E05, 34C07

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-4-352, author = {Liu , ShanshanJin , Xuyi and Xiong , Yujie}, title = {The Number of Limit Cycles in a Class of Piecewise Polynomial Systems}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2022}, volume = {4}, number = {2}, pages = {352--370}, abstract = {

In this paper, we pay attention to the number of limit cycles for a class of piecewise smooth near-Hamiltonian systems. By using the expression of the first order Melnikov function and some known results about Chebyshev systems, we study upper bound of the number of limit cycles in Hopf bifurcation and Poincaré bifurcation respectively.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2022.352}, url = {http://global-sci.org/intro/article_detail/jnma/20712.html} }
TY - JOUR T1 - The Number of Limit Cycles in a Class of Piecewise Polynomial Systems AU - Liu , Shanshan AU - Jin , Xuyi AU - Xiong , Yujie JO - Journal of Nonlinear Modeling and Analysis VL - 2 SP - 352 EP - 370 PY - 2022 DA - 2022/06 SN - 4 DO - http://doi.org/10.12150/jnma.2022.352 UR - https://global-sci.org/intro/article_detail/jnma/20712.html KW - Piecewise smooth system, Melnikov function, ECT-system, Limit cycle. AB -

In this paper, we pay attention to the number of limit cycles for a class of piecewise smooth near-Hamiltonian systems. By using the expression of the first order Melnikov function and some known results about Chebyshev systems, we study upper bound of the number of limit cycles in Hopf bifurcation and Poincaré bifurcation respectively.

Shanshan Liu, Xuyi Jin & Yujie Xiong. (2022). The Number of Limit Cycles in a Class of Piecewise Polynomial Systems. Journal of Nonlinear Modeling and Analysis. 4 (2). 352-370. doi:10.12150/jnma.2022.352
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