Hopf Bifurcation Analysis of a Delayed Diffusive Predator-Prey Model with Predator Interference or Foraging Facilitation

A delayed diffusive predator-prey model with predator interference or foraging facilitation is studied. We are interested in the existence of Turing instability, local stability, and Hopf bifurcation. We analyze the direction and stability of bifurcating periodic solutions by the normal form method....

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Bibliographic Details
Published in:Discrete dynamics in nature and society 2022, Vol.2022 (1)
Main Authors: Wang, Wenlong, Liu, Zijun, Yang, Ruizhi
Format: Article
Language:English
Subjects:
Applied mathematics
Biology
Canonical forms
Equilibrium
Hopf bifurcation
Interference
Population
Predator-prey simulation
Predators
Stability analysis
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Summary:A delayed diffusive predator-prey model with predator interference or foraging facilitation is studied. We are interested in the existence of Turing instability, local stability, and Hopf bifurcation. We analyze the direction and stability of bifurcating periodic solutions by the normal form method. Our results suggest that diffusion can induce Turing instability and time delay can induce oscillation of prey and predator’s densities. In addition, the interference parameter λ0 has stabilizing and destabilizing effect on the positive equilibrium.
ISSN:1026-0226
1607-887X
DOI:10.1155/2022/5278036