We studied the fear effect of predator-prey model and the system effect of shelter,and established a class of modified Leslie-Gower predator-prey models with fear effects,shelter-like comparison theorem using differential equation,and rate-dependent functional responses.We proved that the boundedness of the model solutions and gived sufficient conditions for the existence of the equilibrium point.Using the linearization method,we analyzed the local stability of the equilibrium point analyzed the Hopf bifurcation of the model.The sufficient conditions for the Hopf bifurcation are given by calculating the first Lyapunov-coefficient.The directionality and stability of bifurcation are discussed and the theoretical results are verified by numerical simulation.
关键词
恐惧效应/Leslie-Gower捕食者-食饵模型/避难所/比率依赖型/Hopf分岔/稳定性
Key words
fear effect/modified Leslie-Gower model/shelter/rate-dependent/Hopf bifurcation/stability
维普
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