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Hopf bifurcations in a predator-prey system of population allelopathy with a discrete delay and a distributed delay

A delayed Lotka–Volterra predator-prey system of population allelopathy with discrete delay and distributed maturation delay for the predator population described by an integral with a strong delay kernel is considered. By linearizing the system at the positive equilibrium and analyzing the associat... Full description

Journal Title: Nonlinear Dynamics 2012, Vol.69(4), pp.2155-2167
Main Author: Wang, Xinhui
Other Authors: Liu, Haihong , Xu, Chenglin
Format: Electronic Article Electronic Article
Language: English
Subjects:
ID: ISSN: 0924-090X ; E-ISSN: 1573-269X ; DOI: 10.1007/s11071-012-0416-0
Link: http://dx.doi.org/10.1007/s11071-012-0416-0
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recordid: springer_jour10.1007/s11071-012-0416-0
title: Hopf bifurcations in a predator-prey system of population allelopathy with a discrete delay and a distributed delay
format: Article
creator:
  • Wang, Xinhui
  • Liu, Haihong
  • Xu, Chenglin
subjects:
  • Lotka–Volterra predator-prey system
  • Discrete delay
  • Distributed delay
  • Stability
  • Hopf bifurcation
  • Periodic solution
ispartof: Nonlinear Dynamics, 2012, Vol.69(4), pp.2155-2167
description: A delayed Lotka–Volterra predator-prey system of population allelopathy with discrete delay and distributed maturation delay for the predator population described by an integral with a strong delay kernel is considered. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equation, the asymptotic stability of the positive equilibrium is investigated and Hopf bifurcations are demonstrated. Furthermore, the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem for functional differential equations. Finally, some numerical simulations are carried out for illustrating the theoretical results.
language: eng
source:
identifier: ISSN: 0924-090X ; E-ISSN: 1573-269X ; DOI: 10.1007/s11071-012-0416-0
fulltext: fulltext
issn:
  • 1573-269X
  • 1573269X
  • 0924-090X
  • 0924090X
url: Link


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titleHopf bifurcations in a predator-prey system of population allelopathy with a discrete delay and a distributed delay
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subjectLotka–Volterra predator-prey system ; Discrete delay ; Distributed delay ; Stability ; Hopf bifurcation ; Periodic solution
descriptionA delayed Lotka–Volterra predator-prey system of population allelopathy with discrete delay and distributed maturation delay for the predator population described by an integral with a strong delay kernel is considered. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equation, the asymptotic stability of the positive equilibrium is investigated and Hopf bifurcations are demonstrated. Furthermore, the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem for functional differential equations. Finally, some numerical simulations are carried out for illustrating the theoretical results.
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titleHopf bifurcations in a predator-prey system of population allelopathy with a discrete delay and a distributed delay
descriptionA delayed Lotka–Volterra predator-prey system of population allelopathy with discrete delay and distributed maturation delay for the predator population described by an integral with a strong delay kernel is considered. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equation, the asymptotic stability of the positive equilibrium is investigated and Hopf bifurcations are demonstrated. Furthermore, the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem for functional differential equations. Finally, some numerical simulations are carried out for illustrating the theoretical results.
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abstractA delayed Lotka–Volterra predator-prey system of population allelopathy with discrete delay and distributed maturation delay for the predator population described by an integral with a strong delay kernel is considered. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equation, the asymptotic stability of the positive equilibrium is investigated and Hopf bifurcations are demonstrated. Furthermore, the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem for functional differential equations. Finally, some numerical simulations are carried out for illustrating the theoretical results.
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pubSpringer Netherlands
doi10.1007/s11071-012-0416-0
pages2155-2167
date2012-09