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Multiple Limit Cycles Bifurcation From the Degenerate Singularity for a Class of Three-dimensional Systems

Multiple Limit Cycles Bifurcation From the Degenerate Singularity for a Class of Three-dimensional Systems
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摘要 In this paper,bifurcation of small amplitude limit cycles from the degenerate equilibrium of a three-dimensional system is investigated.Firstly,the method to calculate the focal values at nilpotent critical point on center manifold is discussed.Then an example is studied,by computing the quasi-Lyapunov constants,the existence of at least 4 limit cycles on the center manifold is proved.In terms of degenerate singularity in high-dimensional systems,our work is new. In this paper,bifurcation of small amplitude limit cycles from the degenerate equilibrium of a three-dimensional system is investigated.Firstly,the method to calculate the focal values at nilpotent critical point on center manifold is discussed.Then an example is studied,by computing the quasi-Lyapunov constants,the existence of at least 4 limit cycles on the center manifold is proved.In terms of degenerate singularity in high-dimensional systems,our work is new.
作者 Qin-long WANG Wen-tao HUANG Yi-rong LIU
机构地区 School of Science Mathematics School of Central South University
出处 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2016年第1期73-80,共8页 应用数学学报（英文版）
基金 Supported by Natural Science Foundation of China grants 11461021,11261013 Nature Science Foundation of Guangxi(2015GXNSFAA139011) the Scientific Research Foundation of Guangxi Education Department(ZD2014131) Guangxi Education Department Key Laboratory of Symbolic Computation and Engineering Processing
关键词 Quasi-Lyapunov constant degenerate singularity limit cycles bifurcation three-dimensional system Quasi-Lyapunov constant degenerate singularity limit cycles bifurcation three-dimensional system
分类号 O175 [理学—基础数学]
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参考文献15

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Acta Mathematicae Applicatae Sinica
2016年 第1期

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