AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
Powered by AMiner. Clicking this button will take you away from SciOpen.
Home Networks and Heterogeneous Media Article
PDF (287 KB)
Cite
EndNote(RIS) BibTeX
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
Research Article | Open Access

On the number of limit cycles of a class of near-Hamiltonian systems near a degenerate center

School of Mathematics and Statistics, Linyi University, Linyi, Shandong 276000, PR China
Show Author Information

Abstract

In this paper, we focused on studying the number of limit cycles of a class of near-Hamiltonian systems, whose unperturbed system possesses a degenerate center. Using the first order Melnikov function, we obtained the lower bound of the maximum number of limit cycles in Poincaré bifurcation under certain conditions. In addition, we obtained the number of small-amplitude limit cycles that bifurcate from the degenerate center. We also provided two examples as applications.

Keywords

BifurcationMelnikov functionlimit cyclesdegenerate centernear-Hamiltonian system

References

【1】
【1】
 
 
Crossref Google Scholar
Networks and Heterogeneous Media
Volume 20 Issue 4,
October 2025
Pages 1175-1189
DOI: 10.3934/nhm.2025050

{{item.num}}

Comments on this article

Go to comment

< Back to all reports

Review Status: {{reviewData.commendedNum}} Commended , {{reviewData.revisionRequiredNum}} Revision Required , {{reviewData.notCommendedNum}} Not Commended Under Peer Review

Review Comment

Cite this Report
Close
Close
Cite this article:
Cai M. On the number of limit cycles of a class of near-Hamiltonian systems near a degenerate center. Networks and Heterogeneous Media, 2025, 20(4): 1175-1189. https://doi.org/10.3934/nhm.2025050

59

Views

1

Downloads

0

Crossref

0

Web of Science

0

Scopus
Received: 25 July 2025
Revised: 28 September 2025
Accepted: 22 October 2025
Published: 15 October 2025
©2025 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)