Hopf bifurcation in a delayed prey-predator model with prey refuge involving fear effect  

作　　者：Ankit Parwaliya Anuraj Singh Ajay Kumar 

机构地区：[1]Department of Applied Sciences,ABV-Indian Institute of Information Technology and Management,Gwalior 474015,India

出　　处：《International Journal of Biomathematics》2024年第5期1-32,共32页生物数学学报（英文版）

基　　金：supported by MATRICS,Science Engineering Research Board,Government of India(MTR/2020/000477).

摘　　要：This work investigates a prey-predator model featuring a Holling-type II functional response,in which the fear effect of predation on the prey species,as well as prey refuge,are considered.Specifically,the model assumes that the growth rate of the prey population decreases as a result of the fear of predators.Moreover,the detection of the predator by the prey species is subject to a delay known as the fear response delay,which is incorporated into the model.The paper establishes the preliminary conditions for the solution of the delayed model,including positivity,boundedness and permanence.The paper discusses the existence and stability of equilibrium points in the model.In particular,the paper considers the discrete delay as a bifurcation parameter,demonstrating that the system undergoes Hopf bifurcation at a critical value of the delay parameter.The direction and stability of periodic solutions are determined using central manifold and normal form theory.Additionally,the global stability of the model is established at axial and positive equilibrium points.An extensive numerical simulation is presented to validate the analytical findings,including the continuation of the equilibrium branch for positive equilibrium points.

关 键 词：Hopf bifurcation fear effect prey refuge periodic solutions time delay branch off 

分 类 号：O17[理学—数学]