In this paper, some feasibly suffcient conditions are obtained for the global asymptotic stability of a positive steady state of a predator-prey system with stage structure for the predator by using the theory of comp...In this paper, some feasibly suffcient conditions are obtained for the global asymptotic stability of a positive steady state of a predator-prey system with stage structure for the predator by using the theory of competitive systems, compound matrices and stability of periodic orbits, and then the work of Wang [4] is improved.展开更多
In this paper the dynamical behaviors of a predator-prey system with Holling Type-Ⅳ functionalresponse are investigated in detail by using the analyses of qualitative method,bifurcation theory,and numericalsimulation...In this paper the dynamical behaviors of a predator-prey system with Holling Type-Ⅳ functionalresponse are investigated in detail by using the analyses of qualitative method,bifurcation theory,and numericalsimulation.The qualitative analyses and numerical simulation for the model indicate that it has a unique stablelimit cycle.The bifurcation analyses of the system exhibit static and dynamical bifurcations including saddle-node bifurcation,Hopf bifurcation,homoclinic bifurcation and bifurcation of cusp-type with codimension two(ie,the Bogdanov-Takens bifurcation),and we show the existence of codimension three degenerated equilibriumand the existence of homoclinic orbit by using numerical simulation.展开更多
基金supported by National Natural Science Foundation of China
文摘In this paper, some feasibly suffcient conditions are obtained for the global asymptotic stability of a positive steady state of a predator-prey system with stage structure for the predator by using the theory of competitive systems, compound matrices and stability of periodic orbits, and then the work of Wang [4] is improved.
基金Supported by Chinese Academy of Sciences (KZCX2-SW-118)Supported by the NNSF of China (No.10071027No.10231020)
文摘In this paper the dynamical behaviors of a predator-prey system with Holling Type-Ⅳ functionalresponse are investigated in detail by using the analyses of qualitative method,bifurcation theory,and numericalsimulation.The qualitative analyses and numerical simulation for the model indicate that it has a unique stablelimit cycle.The bifurcation analyses of the system exhibit static and dynamical bifurcations including saddle-node bifurcation,Hopf bifurcation,homoclinic bifurcation and bifurcation of cusp-type with codimension two(ie,the Bogdanov-Takens bifurcation),and we show the existence of codimension three degenerated equilibriumand the existence of homoclinic orbit by using numerical simulation.
