Electron. J. Differential Equations, Vol. 2021 (2021), No. 42, pp. 1-16.

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

Yuting Cai, Chuncheng Wang, Dejun Fan

Abstract:
In this article, we study a predator-prey model with age structure, Holling-type IV response, and two time delays. By an algebraic method, we determine all the critical values for these two delays, such that the characteristic equation has purely imaginary roots. This provides a sharp stability region on the parameter plane of the positive equilibrium. Applying integrated semigroup theory and Hopf bifurcation theorem for abstract Cauchy problems with non-dense domain, we can show the occurrence of Hopf bifurcation as the time delays pass through these critical values. In particular, the phenomenon of stability switches can also be observed as the time delays vary. Numerical simulations are carried out to illustrate the theoretical results.

Submitted January 15, 2020. Published May 14, 2021.
Math Subject Classifications: 37G10, 35F31.
Key Words: Age-structured model; Hopf bifurcation; Holling-type IV response.
DOI: https://doi.org/10.58997/ejde.2021.42

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Yuting Cai School of Mathematics
Harbin Institute of Technology
Harbin, Heilongjiang, 150001, China
email: 514935056@qq.com
Chuncheng Wang
School of Mathematics
Harbin Institute of Technology
Harbin, Heilongjiang, 150001, China
email: wangchuncheng@hit.edu.cn
Dejun Fan
School of Mathematics
Harbin Institute of Technology (Weihai)
Weihai, Shandong, 264209, China
email: dejun_fan@163.com

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