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

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 glob...

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Bibliographic Details
Published inAIMS mathematics Vol. 8; no. 9; pp. 21943 - 21967
Main Authors Wu, Ming, Yao, Hongxing
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2023
Subjects
bifurcation
delay
diffusion
stability
toxins
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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.20231119