Dynamics of a diffusive two predators- one prey system




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


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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2023 Dec 28

How to Cite

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



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

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