Spatiotemporal dynamics of a predator-prey model with a gestation delay and nonlocal competition

Wenbin Zhong; Yuting Ding; Wenbin Zhong; Yuting Ding

doi:10.3934/era.2025116

Electronic Research Archive

2025, Volume 33, Issue 4: 2601-2617. doi: 10.3934/era.2025116

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Research article

Spatiotemporal dynamics of a predator-prey model with a gestation delay and nonlocal competition

Wenbin Zhong ,
Yuting Ding ^,

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

Received: 21 February 2025 Revised: 24 March 2025 Accepted: 28 March 2025 Published: 28 April 2025

Predator gestation delay and nonlocal competition play key roles in controlling population density and maintaining ecosystem stability. In order to control the Dendrolimus superans that cause serious damage to forests, we propose a predator-prey reaction-diffusion equation with Holling type-II functional response function, gestation delay, and nonlocal competition. We investigated the existence conditions of the Hopf bifurcation and obtained its normal form of Hopf bifurcation by employing the multiple time scales method. We selected the appropriate parameters for numerical simulation and found that the gestation delay is helpful to maintain the stability of the population density of Dendrolimus superans.
- prey-predator model,
- nonlocal competition,
- Holling type-II functional response,
- Hopf bifurcation,
- gestation delay
Citation: Wenbin Zhong, Yuting Ding. Spatiotemporal dynamics of a predator-prey model with a gestation delay and nonlocal competition[J]. Electronic Research Archive, 2025, 33(4): 2601-2617. doi: 10.3934/era.2025116

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Abstract

Predator gestation delay and nonlocal competition play key roles in controlling population density and maintaining ecosystem stability. In order to control the Dendrolimus superans that cause serious damage to forests, we propose a predator-prey reaction-diffusion equation with Holling type-II functional response function, gestation delay, and nonlocal competition. We investigated the existence conditions of the Hopf bifurcation and obtained its normal form of Hopf bifurcation by employing the multiple time scales method. We selected the appropriate parameters for numerical simulation and found that the gestation delay is helpful to maintain the stability of the population density of Dendrolimus superans.

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