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Research Article | Open Access

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

Ming Wu1,2, Hongxing Yao1( )
School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, China
Faculty of Science, Jinling Institute of Technology, Nanjing 211169, China
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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.

Keywords

toxinsstabilitydiffusiondelaybifurcation
CLC number: 34K18, 35B32

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AIMS Mathematics
Volume 8 Issue 9,
September 2023
Pages 21943-21967
DOI: 10.3934/math.20231119

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Cite this article:
Wu M, Yao H. Stability and bifurcation of a delayed diffusive predator-prey model affected by toxins. AIMS Mathematics, 2023, 8(9): 21943-21967. https://doi.org/10.3934/math.20231119

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Received: 07 April 2023
Revised: 30 June 2023
Accepted: 02 July 2023
Published: 15 September 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)