Dynamics and bifurcations of a modified Leslie‐Gower–type model considering a Beddington‐DeAngelis functional response

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 o...

Full description

Saved in:
Bibliographic Details
Published inMathematical methods in the applied sciences Vol. 42; no. 9; pp. 3179 - 3210
Main Authors Vera‐Damián, Yrina, Vidal, Claudio, González‐Olivares, Eduardo
Format Journal Article
LanguageEnglish
Published Freiburg Wiley Subscription Services, Inc 01.06.2019
Subjects
Beddington‐DeAngelis functional response
Bifurcations
Bogdanov‐Takens bifurcation
Computer simulation
Differential equations
Ecological effects
Ecological monitoring
homoclinic bifurcation
Hopf bifurcation
limit cycles
Mathematical models
Ordinary differential equations
Predator-prey simulation
predator‐prey model
stability
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.5577