Dynamics of a diffusive two predators- one prey system

Authors

  • Debasis Mukherjee Department of Mathematics, Vivekananda College, Thakurpukur, Kolkata-700063, India

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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Published

2023 Dec 28

How to Cite

[1]
D. Mukherjee, “Dynamics of a diffusive two predators- one prey system ”, Electron. J. Appl. Math., vol. 1, no. 3, pp. 47–60, Dec. 2023.

Issue

Section

Research Article
Received 2023 Oct 06
Accepted 2023 Dec 27
Published 2023 Dec 28