New configurations of 24 limit cycles in a quintic system

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• 作者：Yuhai Wu ; Maoan Han
• 关键词：Double homoclinic loops ; Bifurcation ; Melnikov function ; Stability ; Limit cycles
• 刊名：Computers and Mathematics with Applications
• 出版年：2008
• 期刊代码：37_08981221
• 类别：cp
• 出版时间：May 2008
• 卷：55
• 期：9
• 页码：2064-2075
• 文件大小：523 K

摘要

This paper concerns with the number and distributions of limit cycles in a yle="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6TYJ-4R2HKR3-2&_mathId=mml1&_user=1067359&_cdi=5620&_rdoc=15&_acct=C000050221&_version=1&_userid=10&md5=6a9cf89ac546499828963bcc876ec2d6" title="Click to view the MathML source" alt="Click to view the MathML source">Z₃-equivariant quintic planar polynomial system. 24 limit cycles are found in this system and two different configurations of them are shown by combining the methods of double homoclinic loops bifurcation, Poincaré bifurcation and qualitative analysis. The two configurations of 24 limit cycles obtained in this paper are new. The results obtained are useful to the study of weakened 16th Hilbert Problem.