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Vera-Damian, Y., Vidal, C., & Gonzalez-Olivares, E. (2019). Dynamics and bifurcations of a modified Leslie-Gower-type model considering a Beddington-DeAngelis functional response. Math. Meth. Appl. Sci., 42(9), 3179–3210.
Abstract: In this paper, a planar system of ordinary differential equations is considered, which is a modified Leslie-Gower model, considering a Beddington-DeAngelis functional response. It generates a complex dynamics of the predator-prey interactions according to the associated parameters. From the system obtained, we characterize all the equilibria and its local behavior, and the existence of a trapping set is proved. We describe different types of bifurcations (such as Hopf, Bogdanov-Takens, and homoclinic bifurcation), and the existence of limit cycles is shown. Analytic proofs are provided for all results. Ecological implications and a set of numerical simulations supporting the mathematical results are also presented.
Keywords: Beddington-DeAngelis functional response; Bogdanov-Takens bifurcation; homoclinic bifurcation; Hopf bifurcation; limit cycles; predator-prey model; stability