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

Peng Feng, Yun Kang

Research output: Contribution to journalArticle

22 Scopus citations

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 - Jan 1 2015

Keywords

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

ASJC Scopus subject areas

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

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