Stability and Hopf bifurcation analysis for a Lotka-Volterra predator-prey model with two delays

Changjin Xu; Maoxin Liao; Xiaofei He

International Journal of Applied Mathematics and Computer Science (2011)

  • Volume: 21, Issue: 1, page 97-107
  • ISSN: 1641-876X

Abstract

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In this paper, a two-species Lotka-Volterra predator-prey model with two delays is considered. By analyzing the associated characteristic transcendental equation, the linear stability of the positive equilibrium is investigated and Hopf bifurcation is demonstrated. Some explicit formulae for determining the stability and direction of Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using normal form theory and center manifold theory. Some numerical simulations for supporting the theoretical results are also included.

How to cite

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Changjin Xu, Maoxin Liao, and Xiaofei He. "Stability and Hopf bifurcation analysis for a Lotka-Volterra predator-prey model with two delays." International Journal of Applied Mathematics and Computer Science 21.1 (2011): 97-107. <http://eudml.org/doc/208040>.

@article{ChangjinXu2011,
abstract = {In this paper, a two-species Lotka-Volterra predator-prey model with two delays is considered. By analyzing the associated characteristic transcendental equation, the linear stability of the positive equilibrium is investigated and Hopf bifurcation is demonstrated. Some explicit formulae for determining the stability and direction of Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using normal form theory and center manifold theory. Some numerical simulations for supporting the theoretical results are also included.},
author = {Changjin Xu, Maoxin Liao, Xiaofei He},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {predator-prey model; delay; stability; Hopf bifurcation},
language = {eng},
number = {1},
pages = {97-107},
title = {Stability and Hopf bifurcation analysis for a Lotka-Volterra predator-prey model with two delays},
url = {http://eudml.org/doc/208040},
volume = {21},
year = {2011},
}

TY - JOUR
AU - Changjin Xu
AU - Maoxin Liao
AU - Xiaofei He
TI - Stability and Hopf bifurcation analysis for a Lotka-Volterra predator-prey model with two delays
JO - International Journal of Applied Mathematics and Computer Science
PY - 2011
VL - 21
IS - 1
SP - 97
EP - 107
AB - In this paper, a two-species Lotka-Volterra predator-prey model with two delays is considered. By analyzing the associated characteristic transcendental equation, the linear stability of the positive equilibrium is investigated and Hopf bifurcation is demonstrated. Some explicit formulae for determining the stability and direction of Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using normal form theory and center manifold theory. Some numerical simulations for supporting the theoretical results are also included.
LA - eng
KW - predator-prey model; delay; stability; Hopf bifurcation
UR - http://eudml.org/doc/208040
ER -

References

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Citations in EuDML Documents

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  1. Kun-Yi Yang, Ling-Li Zhang, Jie Zhang, Stability analysis of a three-dimensional energy demand-supply system under delayed feedback control
  2. Dariusz Myszor, Krzysztof A. Cyran, Mathematical modelling of molecule evolution in protocells
  3. Qiaoling Chen, Zhidong Teng, Zengyun Hu, Bifurcation and control for a discrete-time prey-predator model with Holling-IV functional response
  4. Hasim A. Obaid, Rachid Ouifki, Kailash C. Patidar, An unconditionally stable nonstandard finite difference method applied to a mathematical model of HIV infection

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