Hopf bifurcation analysis in a delayed diffusive predator-prey system with nonlocal competition and generalist predator

Chenxuan Nie; Dan Jin; Ruizhi Yang; Chenxuan Nie; Dan Jin; Ruizhi Yang

doi:10.3934/math.2022737

AIMS Mathematics

2022, Volume 7, Issue 7: 13344-13360. doi: 10.3934/math.2022737

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Research article

Hopf bifurcation analysis in a delayed diffusive predator-prey system with nonlocal competition and generalist predator

Department of Mathematics, Northeast Forestry University, Harbin 150040, China

Received: 22 February 2022 Revised: 24 April 2022 Accepted: 04 May 2022 Published: 17 May 2022
MSC : 34K18, 35B32

A delayed diffusive predator-prey system with nonlocal competition and generalist predators is considered. The local stability of the positive equilibrium and Hopf bifurcation at positive equilibrium is studied by using time delay as a parameter. In addition, the property of Hopf bifurcation is analyzed using the center manifold theorem and normal form method. It is determined that time delays can affect the stability of the positive equilibrium and induce spatial inhomogeneous periodic oscillation of prey and predator population densities.
- predator-prey,
- delay,
- Hopf bifurcation,
- nonlocal competition
Citation: Chenxuan Nie, Dan Jin, Ruizhi Yang. Hopf bifurcation analysis in a delayed diffusive predator-prey system with nonlocal competition and generalist predator[J]. AIMS Mathematics, 2022, 7(7): 13344-13360. doi: 10.3934/math.2022737

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Abstract

A delayed diffusive predator-prey system with nonlocal competition and generalist predators is considered. The local stability of the positive equilibrium and Hopf bifurcation at positive equilibrium is studied by using time delay as a parameter. In addition, the property of Hopf bifurcation is analyzed using the center manifold theorem and normal form method. It is determined that time delays can affect the stability of the positive equilibrium and induce spatial inhomogeneous periodic oscillation of prey and predator population densities.

References

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