Dynamics and bifurcations of a modified Leslie‐Gower–type model considering a Beddington‐DeAngelis functional response. (2nd April 2019)

• Record Type: Journal Article
• Authors: Vera‐Damián, Yrina; Vidal, Claudio; González‐Olivares, Eduardo
• Is Part Of: Mathematical methods in the applied sciences. Volume 42:Number 9(2019)
• Page Start: 3179
• Page End: 3210
• Publication Date: 2019-04-02
• Subjects: Beddington‐DeAngelis functional response -- Bogdanov‐Takens bifurcation -- homoclinic bifurcation -- Hopf bifurcation -- limit cycles -- predator‐prey model -- stability; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5577
• Languages: English
• ISSNs: 0170-4214

Abstract

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.