The center conditions and bifurcation of limit cycles for a class of fifth degree systems are investigated.Two recursive formulas to compute singular quantities at infinity and at the origin are given.The first nine ...The center conditions and bifurcation of limit cycles for a class of fifth degree systems are investigated.Two recursive formulas to compute singular quantities at infinity and at the origin are given.The first nine singular point quantities at infinity and first seven singular point quantities at the origin for the system are given in order to get center conditions and study bifurcation of limit cycles.Two fifth degree systems are constructed.One allows the appearance of eight limit cycles in the neighborhood of infinity,which is the first example that a polynomial differential system bifurcates eight limit cycles at infinity.The other perturbs six limit cycles at the origin.展开更多
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
Based on the relationship between symplectic group Sp（2） and （2）, we provide an intuitive explanation （model） of the 3-dimensional Lagrangian Grassmann manifold （2）, the singular cycles of （2）, and the speci...Based on the relationship between symplectic group Sp（2） and （2）, we provide an intuitive explanation （model） of the 3-dimensional Lagrangian Grassmann manifold （2）, the singular cycles of （2）, and the special Lagrangian Grassmann manifold S（2）. Under this model, we give a formula of the rotation paths defined by Arnold.展开更多
基金Supported by Science Fund of the Education Departmentof Guangxi province( 2 0 0 3) and the NationalNatural Science Foundation of China( 1 0 361 0 0 3)
文摘The center conditions and bifurcation of limit cycles for a class of fifth degree systems are investigated.Two recursive formulas to compute singular quantities at infinity and at the origin are given.The first nine singular point quantities at infinity and first seven singular point quantities at the origin for the system are given in order to get center conditions and study bifurcation of limit cycles.Two fifth degree systems are constructed.One allows the appearance of eight limit cycles in the neighborhood of infinity,which is the first example that a polynomial differential system bifurcates eight limit cycles at infinity.The other perturbs six limit cycles at the origin.
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.
基金The author is grateful to Professor Yiming Long for his interest and Professor Xijun Hu for many useful advises and patient guidance. Also, the author would like to convey thanks to the anonymous referees for useful comments and suggestions. Finally, the author won＇t forget his beloved friends and family members, for their understanding and endless love through the duration of his studies. This work was partially supported by the National Natural Science Foundation of China （Grant No. 11425105）.
文摘Based on the relationship between symplectic group Sp（2） and （2）, we provide an intuitive explanation （model） of the 3-dimensional Lagrangian Grassmann manifold （2）, the singular cycles of （2）, and the special Lagrangian Grassmann manifold S（2）. Under this model, we give a formula of the rotation paths defined by Arnold.
