Double Hopf bifurcation of a diffusive predator–prey system with strong Allee effect and two delays
Articles
Yuying Liu
Harbin Institute of Technology
https://orcid.org/0000-0002-3370-5336
Junjie Wei
Harbin Institute of Technology, Jimei University
Published 2021-01-01
https://doi.org/10.15388/namc.2021.26.20561
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Keywords

predator–prey
strong Allee effect
double Hopf bifurcation
two delays
stability switching curves

How to Cite

Liu Y. and Wei J. (2021) “Double Hopf bifurcation of a diffusive predator–prey system with strong Allee effect and two delays”, Nonlinear Analysis: Modelling and Control, 26(1), pp. 72-92. doi: 10.15388/namc.2021.26.20561.

Abstract

In this paper, we consider a diffusive predator–prey system with strong Allee effect and two delays. First, we explore the stability region of the positive constant steady state by calculating the stability switching curves. Then we derive the Hopf and double Hopf bifurcation theorem via the crossing directions of the stability switching curves. Moreover, we calculate the normal forms near the double Hopf singularities by taking two delays as parameters. We carry out some numerical simulations for illustrating the theoretical results. Both theoretical analysis and numerical simulation show that the system near double Hopf singularity has rich dynamics, including stable spatially homogeneous and inhomogeneous periodic solutions. Finally, we evaluate the influence of two parameters on the existence of double Hopf bifurcation.

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