Stability and bifurcation of a delayed diffusive predator-prey model affected by toxins

Ming Wu; Hongxing Yao; Ming Wu; Hongxing Yao

doi:10.3934/math.20231119

AIMS Mathematics

2023, Volume 8, Issue 9: 21943-21967. doi: 10.3934/math.20231119

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Research article

Stability and bifurcation of a delayed diffusive predator-prey model affected by toxins

Ming Wu ^1,2,
Hongxing Yao ^{1
,
,}

1.
School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, China
2.
Faculty of Science, Jinling Institute of Technology, Nanjing 211169, China

Received: 07 April 2023 Revised: 30 June 2023 Accepted: 02 July 2023 Published: 11 July 2023
MSC : 34K18, 35B32

In this work, a diffusive predator-prey model with the effects of toxins and delay is considered. Initially, we investigated the presence of solutions and the stability of the system. Then, we examined the local stability of the equilibria and Hopf bifurcation generated by delay, as well as the global stability of the equilibria using a Lyapunov function. In addition, we extract additional results regarding the presence and nonexistence of non-constant steady states in this model by taking into account the influence of diffusion. We show several numerical simulations to validate our theoretical findings.
- toxins,
- stability,
- diffusion,
- delay,
- bifurcation
Citation: Ming Wu, Hongxing Yao. Stability and bifurcation of a delayed diffusive predator-prey model affected by toxins[J]. AIMS Mathematics, 2023, 8(9): 21943-21967. doi: 10.3934/math.20231119

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Abstract

In this work, a diffusive predator-prey model with the effects of toxins and delay is considered. Initially, we investigated the presence of solutions and the stability of the system. Then, we examined the local stability of the equilibria and Hopf bifurcation generated by delay, as well as the global stability of the equilibria using a Lyapunov function. In addition, we extract additional results regarding the presence and nonexistence of non-constant steady states in this model by taking into account the influence of diffusion. We show several numerical simulations to validate our theoretical findings.

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