Dynamics of a Diffusive Two Predators-One Prey System

This paper analyses a diffusive predator-prey model consisting of a single prey species and two predator species with modified Leslie-Gower term Holling type II functional response subject to the homogeneous Neumann boundary condition. Local stability condition is derived by the application of Routh...

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Bibliographic Details
Published inElectronic Journal of Applied Mathematics Vol. 1; no. 3; pp. 47 - 60
Main Author Mukherjee, Debasis
Format Journal Article
LanguageEnglish
Published 28.12.2023
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Summary:This paper analyses a diffusive predator-prey model consisting of a single prey species and two predator species with modified Leslie-Gower term Holling type II functional response subject to the homogeneous Neumann boundary condition. Local stability condition is derived by the application of Routh-Hurwitz criterion. Global asymptotic stability of the unique positive steady state is shown by constructing a suitable Lyapunov function when self diffusion is allowed where as non-constant positive steady states can exist due to the presence of cross-diffusion, that means, cross-diffusion can induce stationary pattern. Taking the cross diffusion as a bifurcation parameter, one can show the existence of positive non-constant solutions with the help of bifurcation theory. A brief conclusion completes the paper.
ISSN:2980-2474
2980-2474
DOI:10.61383/ejam.20231349