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 c...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.展开更多
基金Supported by Natural Science Foundation of China grants 11461021,11261013Nature Science Foundation of Guangxi(2015GXNSFAA139011)+1 种基金the Scientific Research Foundation of Guangxi Education Department(ZD2014131)Guangxi Education Department Key Laboratory of Symbolic Computation and Engineering Processing
文摘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.
