Title: Dynamics of a delayed stage structure predator-prey model with predator-dependent prey refuge

Authors: Wensheng Yang; Qi Cao

Addresses: School of Mathematics and Statistics, Fujian Normal University, Fuzhou, Fujian, China ' School of Mathematics and Statistics, Fujian Normal University, Fuzhou, Fujian, China

Abstract: In this paper, a delayed stage structure predator-prey model with predator-dependent prey refuge is proposed. The prey population is divided into two parts: juvenile and adult prey, and the population of predators depends on adult prey only. The number of prey in refugia is nonlinear and depends on the number of predators in this work. First, the existence and local stability of all possible equilibria are investigated. By constructing appropriate Lyapunov functions, we get the sufficient conditions for the global stability of the predator-free equilibrium and the positive equilibrium, respectively. Moreover, we introduce the gestation delay of predator to the system. The existence of periodic solutions at the positive equilibrium point via Hopf-bifurcation with respect to delay is established. The stability and direction of Hopf-bifurcation are also analysed by using Normal form theory and Centre manifold theory.

Keywords: stage-structure model; predator-dependent refuge; time delay; global stability; Hopf bifurcation.

DOI: 10.1504/IJCSM.2024.137264

International Journal of Computing Science and Mathematics, 2024 Vol.19 No.2, pp.107 - 122

Received: 03 Jul 2022
Accepted: 27 Jul 2023
Published online: 08 Mar 2024 *

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