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Dubey, V.P., Kumar, R. and Kumar, D. (2020) Numerical Solution of Time-Fractional Three-Species Food Chain Model Arising in the Realm of Mathematical Ecology. International Journal of Biomathematics, 13, Article 2050011.
https://doi.org/10.1142/s1793524520500114

has been cited by the following article:

• TITLE: Bifurcation and Turing Pattern Formation in a Diffusion Modified Leslie-Gower Predator-Prey Model with Crowley-Martin Functional Response

  AUTHORS: Dong Wang, Yani Ma

  KEYWORDS: Modified Leslie-Gower Model, Crowley-Martin Function Response, Hopf Bifurcation, Transcritical Bifurcation, Turing Instability

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.12 No.6, June 25, 2024

  ABSTRACT: In this paper, we study a modified Leslie-Gower predator-prey model with Smith growth subject to homogeneous Neumann boundary condition, in which the functional response is the Crowley-Martin functional response term. Firstly, for ODE model, the local stability of equilibrium point is given. And by using bifurcation theory and selecting suitable bifurcation parameters, we find many kinds of bifurcation phenomena, including Transcritical bifurcation and Hopf bifurcation. For the reaction-diffusion model, we find that Turing instability occurs. Besides, it is proved that Hopf bifurcation exists in the model. Finally, numerical simulations are presented to verify and illustrate the theoretical results.