Hopf bifurcation of a delayed predator-prey model with Allee effect and anti-predator behavior  

作　　者：Xinyue Xu Yan Meng Yangyang Shao 

机构地区：[1]School of Mathematics and Physics University of Science and Technology Beijing Beijing,100083,P.R.China

出　　处：《International Journal of Biomathematics》2023年第7期111-139,共29页生物数学学报（英文版）

基　　金：This work is jointly supported by the National traditional Medicine Clinical Research Base Business Construction Special Topics(JDZX2015299);the Fundamental Research Funds for the Central University FRF-BR-16-019A.

摘　　要：This paper proposes a diffusive predator-prey model with Allee effect,time delay and anti-predator behavior.First,the existence and stability of all equilibria are analyzed and the conditions for the appearance of the Hopf bifurcation are studied.Using the normal form and center manifold theory,the formulas which can determine the direction,period and stability of Hopf bifurcation are obtained.Numerical simulations show that the Allee effect can determine the survival abundance of the prey and predator populations,and anti-predator behavior can greatly improve the stability of the coexisting equilibrium.

关 键 词：PREDATOR-PREY Hopf bifurcation delay and diffusion Allee effect numerical simulation 

分 类 号：O175[理学—数学]