**Global stability of a stage-structured predator-prey model with prey dispersal.** / Xu, Rui; Chaplain, M. A. J.; Davidson, F. A.

Research output: Contribution to journal › Article

Xu, R, Chaplain, MAJ & Davidson, FA 2005, 'Global stability of a stage-structured predator-prey model with prey dispersal' *Applied Mathematics and Computation*, vol 171, no. 1, pp. 293-314.

Xu, R., Chaplain, M. A. J., & Davidson, F. A. (2005). Global stability of a stage-structured predator-prey model with prey dispersal. *Applied Mathematics and Computation*, 171(1), 293-314doi: 10.1016/j.amc.2005.01.055

Xu R, Chaplain MAJ, Davidson FA. Global stability of a stage-structured predator-prey model with prey dispersal. Applied Mathematics and Computation. 2005;171(1):293-314.

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title = "Global stability of a stage-structured predator-prey model with prey dispersal",

author = "Rui Xu and Chaplain, {M. A. J.} and Davidson, {F. A.}",

note = "dc.publisher: Elsevier",

year = "2005",

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journal = "Applied Mathematics and Computation",

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TY - JOUR

T1 - Global stability of a stage-structured predator-prey model with prey dispersal

A1 - Xu,Rui

A1 - Chaplain,M. A. J.

A1 - Davidson,F. A.

AU - Xu,Rui

AU - Chaplain,M. A. J.

AU - Davidson,F. A.

PY - 2005

Y1 - 2005

N2 - A delayed Lotka–Volterra type predator-prey model with stage structure for predator and prey dispersal in two-patch environments is investigated. It is assumed that immature individuals and mature individuals of predator species are divided by a fixed age, and that immature predators do not feed on prey and do not have the ability to reproduce; on the other hand, it is assumed that the prey species can disperse between one patch with a low level of food and without predation and one patch with a higher level of food but with predation. By means of two different kinds of Lyapunov functionals, sufficient conditions are derived respectively for the global asymptotic stability of a positive equilibrium of the model. By analyzing the characteristic equation, criterion is established for the local stability of the positive equilibrium. Numerical simulations are presented to illustrate our main results.

AB - A delayed Lotka–Volterra type predator-prey model with stage structure for predator and prey dispersal in two-patch environments is investigated. It is assumed that immature individuals and mature individuals of predator species are divided by a fixed age, and that immature predators do not feed on prey and do not have the ability to reproduce; on the other hand, it is assumed that the prey species can disperse between one patch with a low level of food and without predation and one patch with a higher level of food but with predation. By means of two different kinds of Lyapunov functionals, sufficient conditions are derived respectively for the global asymptotic stability of a positive equilibrium of the model. By analyzing the characteristic equation, criterion is established for the local stability of the positive equilibrium. Numerical simulations are presented to illustrate our main results.

KW - Stage structure

KW - Time delay

KW - Dispersal

KW - Permanence

KW - Global stability

U2 - 10.1016/j.amc.2005.01.055

DO - 10.1016/j.amc.2005.01.055

M1 - Article

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

IS - 1

VL - 171

SP - 293

EP - 314

ER -