Dynamics of a modified Leslie–Gower model with double Allee effects

Peng Feng, Yun Kang

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

Bifurcation analysis of a class of modified Leslie–Gower model with Allee effects in both predator and prey species is given in detail. We show the existence of a heteroclinic separatrix that divides the dynamics of the predator and prey populations and considers the Hopf bifurcation around the interior positive equilibrium. We show that when there are two interior equilibria, the smaller equilibrium is always a saddle, and the larger equilibrium can be either an attractor or a repeller surrounded by a limit cycle. Combining mathematical analysis and numerical simulation, we show that the double Allee effects greatly alter the outcome of the survival of both species.

Original languageEnglish (US)
Pages (from-to)1051-1062
Number of pages12
JournalNonlinear Dynamics
Volume80
Issue number1-2
DOIs
StatePublished - 2015

Fingerprint

Allee Effect
Hopf bifurcation
Computer simulation
Predator
Prey
Interior
Separatrix
Bifurcation Analysis
Saddle
Mathematical Analysis
Model
Limit Cycle
Hopf Bifurcation
Divides
Attractor
Numerical Simulation

Keywords

  • Allee effect
  • Hopf bifurcation
  • Leslie–Gower
  • Predator–prey model

ASJC Scopus subject areas

  • Applied Mathematics
  • Mechanical Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Electrical and Electronic Engineering
  • Control and Systems Engineering

Cite this

Dynamics of a modified Leslie–Gower model with double Allee effects. / Feng, Peng; Kang, Yun.

In: Nonlinear Dynamics, Vol. 80, No. 1-2, 2015, p. 1051-1062.

Research output: Contribution to journalArticle

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