Stability and bifurcation in a delayed predator-prey model with Holling-type IV response function and age structure
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Date
2021-05-14
Authors
Cai, Yuting
Wang, Chuncheng
Fan, Dejun
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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.
Description
Keywords
Age-structured model, Hopf bifurcation, Holling-type IV response
Citation
Cai, Y., Wang, C., & Fan, D. (2021). Stability and bifurcation in a delayed predator-prey model with Holling-type IV response function and age structure. <i>Electronic Journal of Differential Equations, 2021</i>(42), pp. 1-16.
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Attribution 4.0 International