A diffusive predator-prey model with generalist predator and time delay

Ruizhi Yang; Dan Jin; Wenlong Wang; Ruizhi Yang; Dan Jin; Wenlong Wang

doi:10.3934/math.2022255

AIMS Mathematics

2022, Volume 7, Issue 3: 4574-4591. doi: 10.3934/math.2022255

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Research article

A diffusive predator-prey model with generalist predator and time delay

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

Received: 27 October 2021 Revised: 11 December 2021 Accepted: 13 December 2021 Published: 23 December 2021
MSC : 34K18, 35B32

Time delay in the resource limitation of the prey is incorporated into a diffusive predator-prey model with generalist predator. By analyzing the eigenvalue spectrum, time delay inducing instability and Hopf bifurcation are investigated. Some conditions for determining the bifurcation direction and the stability of the bifurcating periodic solution are obtained by utilizing the normal form method and center manifold reduction for partial functional differential equation. The results suggest that time delay can destabilize the stability of coexisting equilibrium and induce bifurcating periodic solution when it increases through a certain threshold.
- delay,
- generalist predator,
- Hopf bifurcation,
- stability
Citation: Ruizhi Yang, Dan Jin, Wenlong Wang. A diffusive predator-prey model with generalist predator and time delay[J]. AIMS Mathematics, 2022, 7(3): 4574-4591. doi: 10.3934/math.2022255

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Abstract

Time delay in the resource limitation of the prey is incorporated into a diffusive predator-prey model with generalist predator. By analyzing the eigenvalue spectrum, time delay inducing instability and Hopf bifurcation are investigated. Some conditions for determining the bifurcation direction and the stability of the bifurcating periodic solution are obtained by utilizing the normal form method and center manifold reduction for partial functional differential equation. The results suggest that time delay can destabilize the stability of coexisting equilibrium and induce bifurcating periodic solution when it increases through a certain threshold.

References

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