Global stability and Hopf bifurcation in a delayed diffusive lesliegower Predator-prey system

Shanshan Chen; Junping Shi; Junjie Wei

doi:10.1142/S0218127412500617

Global stability and Hopf bifurcation in a delayed diffusive lesliegower Predator-prey system

Shanshan Chen^*
, Junping Shi
, Junjie Wei

^*Corresponding author for this work

School of Science

College of William and Mary
Harbin Institute of Technology

Research output: Contribution to journal › Article › peer-review

89 Scopus citations

Abstract

In this paper, we consider a delayed diffusive LeslieGower predator-prey system with homogeneous Neumann boundary conditions. The stability/instability of the coexistence equilibrium and associated Hopf bifurcation are investigated by analyzing the characteristic equations. Furthermore, using the upper and lower solutions method, we give a sufficient condition on parameters so that the coexistence equilibrium is globally asymptotically stable.

Original language	English
Article number	1250061
Journal	International Journal of Bifurcation and Chaos
Volume	22
Issue number	3
DOIs	https://doi.org/10.1142/S0218127412500617
State	Published - Mar 2012

Keywords

Hopf bifurcation
Predator-prey
delay
global stability
reaction-diffusion

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10.1142/S0218127412500617

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title = "Global stability and Hopf bifurcation in a delayed diffusive lesliegower Predator-prey system",

abstract = "In this paper, we consider a delayed diffusive LeslieGower predator-prey system with homogeneous Neumann boundary conditions. The stability/instability of the coexistence equilibrium and associated Hopf bifurcation are investigated by analyzing the characteristic equations. Furthermore, using the upper and lower solutions method, we give a sufficient condition on parameters so that the coexistence equilibrium is globally asymptotically stable.",

keywords = "Hopf bifurcation, Predator-prey, delay, global stability, reaction-diffusion",

author = "Shanshan Chen and Junping Shi and Junjie Wei",

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AU - Chen, Shanshan

AU - Shi, Junping

AU - Wei, Junjie

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N2 - In this paper, we consider a delayed diffusive LeslieGower predator-prey system with homogeneous Neumann boundary conditions. The stability/instability of the coexistence equilibrium and associated Hopf bifurcation are investigated by analyzing the characteristic equations. Furthermore, using the upper and lower solutions method, we give a sufficient condition on parameters so that the coexistence equilibrium is globally asymptotically stable.

AB - In this paper, we consider a delayed diffusive LeslieGower predator-prey system with homogeneous Neumann boundary conditions. The stability/instability of the coexistence equilibrium and associated Hopf bifurcation are investigated by analyzing the characteristic equations. Furthermore, using the upper and lower solutions method, we give a sufficient condition on parameters so that the coexistence equilibrium is globally asymptotically stable.

KW - Hopf bifurcation

KW - Predator-prey

KW - delay

KW - global stability

KW - reaction-diffusion

UR - https://www.scopus.com/pages/publications/84859870921

U2 - 10.1142/S0218127412500617

DO - 10.1142/S0218127412500617

M3 - 文章

AN - SCOPUS:84859870921

SN - 0218-1274

VL - 22

JO - International Journal of Bifurcation and Chaos

JF - International Journal of Bifurcation and Chaos

IS - 3

M1 - 1250061

ER -

Global stability and Hopf bifurcation in a delayed diffusive lesliegower Predator-prey system

Abstract

Keywords

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