Impact of time delay and cooperation strategy on the stability of a predator-prey model with Holling type III functional response  

作　　者：I.Benamara A.El Abdllaouit J.Mikramt 

机构地区：[1]Laboratory of Mathematics Computer Science&Applications-Security of Information Department of Mathematics,Faculty of Sciences Mohammed V University in Rabat,Morocco

出　　处：《International Journal of Biomathematics》2023年第3期165-193,共29页生物数学学报（英文版）

摘　　要：In this paper,we propose and analyze a delayed predator-prey model with Holling type III functional response taking into account cooperation behavior in predators.The time delay is introduced in the attack rate to represent the time necessary to trigger the attack.Each analytical result is followed by an ecological interpretation.We investigate the effect of hunting cooperation on both the number and the level of positive steady states.We observe that the level of the positive equilibrium decreases when increasing the hunting cooperation parameter.Then,we study the impact of the delay as well as the cooperation in hunting on the dynamics of the system.We prove that the presence of delay in the attack rate induces stability switches around the coexisting equilibrium when predators cooperate.In addition,we consider the discrete delay as a bifurcation parameter and prove that the model undergoes a Hopf-bifurcation at the coexisting equilibrium when the delay crosses some critical values.Numerical simulations are presented to confirm our analytical findings.

关 键 词：Predator-prey system Holling type III discrete delay cooperative hunting HOPF-BIFURCATION switch of stability 

分 类 号：O17[理学—数学]