On the number and distributions of limit cycles in a perturbed Z2 -equivariant planar quintic Hamiltonian system

On the number and distributions of limit cycles in a perturbed Z2 -equivariant planar quintic Hamiltonian system | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 27 October 2025 V1 Latest version Share on On the number and distributions of limit cycles in a perturbed Z2 -equivariant planar quintic Hamiltonian system Authors : Hongxian Zhou 0009-0001-6294-4993 [email protected] and Yajing Yuan Authors Info & Affiliations https://doi.org/10.22541/au.176156289.94244608/v1 178 views 93 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract This paper is concerned with the number and distributions of bifurcated limit cycles of a perturbed Z 2 -equivariant quintic Hamiltonian system. By using the bifurcation theory of planar dynamical system and the method of detection function, 25 limit cycles are found in this special planar polynomial system and two different configurations of them are given by numerical simulations under two different sets of controlled parameters. The two configurations of 25 limit cycles obtained in this paper are new and different from four configurations obtained by Y. Wu, L. Tian and M. Han. The results obtained are useful to the study of weakened Hilbert's 16th problem. Supplementary Material File (zhou.pdf) Download 1.02 MB Information & Authors Information Version history V1 Version 1 27 October 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords bifurcation detection function hamiltonian system limit cycle Authors Affiliations Hongxian Zhou 0009-0001-6294-4993 [email protected] Xuchang University View all articles by this author Yajing Yuan Xuchang University View all articles by this author Metrics & Citations Metrics Article Usage 178 views 93 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Hongxian Zhou, Yajing Yuan. On the number and distributions of limit cycles in a perturbed Z2 -equivariant planar quintic Hamiltonian system. Authorea . 27 October 2025. DOI: https://doi.org/10.22541/au.176156289.94244608/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . Format Please select one from the list RIS (ProCite, Reference Manager) EndNote BibTex Medlars RefWorks Direct import Tips for downloading citations document.getElementById('citMgrHelpLink').addEventListener('click', function() { popupHelp(this.href); return false; }); $(".js__slcInclude").on("change", function(e){ if ($(this).val() == 'refworks') $('#direct').prop("checked", false); $('#direct').prop("disabled", ($(this).val() == 'refworks')); }); View Options View options PDF View PDF Figures Tables Media Share Share Share article link Copy Link Copied! Copying failed. 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