This paper deals with the host-parasitoid model,where the logistic equation governs the host population growth,and a proportion of the host population can find refuge.The equilibrium points'existence,number,and lo...This paper deals with the host-parasitoid model,where the logistic equation governs the host population growth,and a proportion of the host population can find refuge.The equilibrium points'existence,number,and local character are discussed.Taking the parameter regulating the parasitoid's growth as a bifurcation parameter,we prove that Neimark-Sacker and period-doubling bifurcations occur.Despite the complex behavior,it can be proved that the system is permanent,ensuring the long-term survival of both populations.Furthermore,it was observed that the presence of the proportional refuge does not significantly influence the system's behavior compared to the system without aproportional refuge.展开更多
文摘This paper deals with the host-parasitoid model,where the logistic equation governs the host population growth,and a proportion of the host population can find refuge.The equilibrium points'existence,number,and local character are discussed.Taking the parameter regulating the parasitoid's growth as a bifurcation parameter,we prove that Neimark-Sacker and period-doubling bifurcations occur.Despite the complex behavior,it can be proved that the system is permanent,ensuring the long-term survival of both populations.Furthermore,it was observed that the presence of the proportional refuge does not significantly influence the system's behavior compared to the system without aproportional refuge.
