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 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.
