A singularity free cosmological model is obtained in a homogeneous and isotropic background with a specific form of the Hubble parameter in the presence of an interacting dark energy represented by a time-varying cosm...A singularity free cosmological model is obtained in a homogeneous and isotropic background with a specific form of the Hubble parameter in the presence of an interacting dark energy represented by a time-varying cosmological constant in general relativity. Different cases that arose have been extensively studied for different values of the curvature parameter. Some interesting results have been found with this form of the Hubble parameter to meet the possible negative value of the decelera- tion parameter （- 1/3≤ q 〈 0） as the current observations reveal. For some particular values of these parameters, the model reduces to Berman＇s model.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
基金Department of Atomic Energy (DAE),Government of India for financial support through the post-doctoral fellowship of the National board of Higher Mathematics (NBHM)
文摘A singularity free cosmological model is obtained in a homogeneous and isotropic background with a specific form of the Hubble parameter in the presence of an interacting dark energy represented by a time-varying cosmological constant in general relativity. Different cases that arose have been extensively studied for different values of the curvature parameter. Some interesting results have been found with this form of the Hubble parameter to meet the possible negative value of the decelera- tion parameter （- 1/3≤ q 〈 0） as the current observations reveal. For some particular values of these parameters, the model reduces to Berman＇s model.
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.
