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Dynamics and bifurcations of a modified Leslie‐Gower–type model considering a Beddington‐DeAngelis functional response
Author(s) -
VeraDamián Yrina,
Vidal Claudio,
GonzálezOlivares Eduardo
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5577
Subject(s) - mathematics , homoclinic orbit , hopf bifurcation , type (biology) , ordinary differential equation , bifurcation , mathematical proof , limit (mathematics) , set (abstract data type) , limit cycle , mathematical analysis , differential equation , nonlinear system , geometry , ecology , physics , quantum mechanics , computer science , biology , programming language
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.