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