Dynamics of a diffusive  two predators- one prey system

Debasis Mukherjee

doi:10.61383/ejam.20231349

Authors

Debasis Mukherjee Department of Mathematics, Vivekananda College, Thakurpukur, Kolkata-700063, India Corresponding Author https://orcid.org/0000-0002-5149-5985

DOI:

https://doi.org/10.61383/ejam.20231349

Keywords:

Cross-diffusion, Leslie-Gower model, global stability, priori estimates, bifurcation

Abstract

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.

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