Stability and bifurcation in a delayed predator-prey model with Holling-type IV response function and age structure

Electronic Journal of Differential Equations

article

Yuting Cai School of Mathematics¹  Chuncheng Wang²  Dejun Fan³ 

[1] Harbin Institute of Technology Harbin;School of Mathematics Harbin Institute of Technology Harbin;School of Mathematics Harbin Institute of Technology

关键词: Age-structured model;    Hopf bifurcation;    Holling-type IV response.;   

DOI  :  10.58997/ejde.2021.42

学科分类：数学（综合）

来源: Texas State University

【 摘 要 】

In this article, we study a predator-prey model with age structure, Holling-type IVresponse, and two time delays. By an algebraic method, we determine all the criticalvalues for these two delays, such that the characteristic equation has purelyimaginary roots. This provides a sharp stability region on the parameter planeof the positive equilibrium. Applying integrated semigroup theory and Hopfbifurcation theorem for abstract Cauchy problems with non-dense domain,we can show the occurrence of Hopf bifurcation as the time delays passthrough these critical values. In particular, the phenomenon of stability switchescan also be observed as the time delays vary. Numerical simulations are carriedout to illustrate the theoretical results.

【 授权许可】

CC BY