**Global stability of a Lotka-Volterra type predator-prey model with stage structure and time delay.** / Xu, Rui; Chaplain, M. A. J.; Davidson, F. A.

Research output: Contribution to journal › Article

Xu, R, Chaplain, MAJ & Davidson, FA 2004, 'Global stability of a Lotka-Volterra type predator-prey model with stage structure and time delay' *Applied Mathematics and Computation*, vol 159, no. 3, pp. 863-880. DOI: 10.1016/j.amc.2003.11.008

Xu, R., Chaplain, M. A. J., & Davidson, F. A. (2004). *Global stability of a Lotka-Volterra type predator-prey model with stage structure and time delay*. *Applied Mathematics and Computation*, *159*(3), 863-880. DOI: 10.1016/j.amc.2003.11.008

Xu R, Chaplain MAJ, Davidson FA. Global stability of a Lotka-Volterra type predator-prey model with stage structure and time delay. Applied Mathematics and Computation. 2004;159(3):863-880. Available from, DOI: 10.1016/j.amc.2003.11.008

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title = "Global stability of a Lotka-Volterra type predator-prey model with stage structure and time delay",

keywords = "Stage structure, Time delay, Characteristic equation, Global stability",

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

note = "dc.publisher: Elsevier",

year = "2004",

doi = "10.1016/j.amc.2003.11.008",

volume = "159",

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journal = "Applied Mathematics and Computation",

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TY - JOUR

T1 - Global stability of a Lotka-Volterra type predator-prey model with stage structure and time delay

AU - Xu,Rui

AU - Chaplain,M. A. J.

AU - Davidson,F. A.

N1 - dc.publisher: Elsevier

PY - 2004

Y1 - 2004

N2 - A delayed Lotka-Volterra type predator-prey model with stage structure for predator is investigated. It is assumed in the model that the individuals in the predator population may belong to one of two classes: the immatures and the matures, the age to maturity is presented by a time delay, and that the immature predators do not have the ability to prey. By analyzing characteristic equations and using an iterative technique, a set of easily verifiable sufficient conditions are derived for the local and global stability of the nonnegative equilibria of the model. Numerical simulations are carried out to illustrate the validity of our results.

AB - A delayed Lotka-Volterra type predator-prey model with stage structure for predator is investigated. It is assumed in the model that the individuals in the predator population may belong to one of two classes: the immatures and the matures, the age to maturity is presented by a time delay, and that the immature predators do not have the ability to prey. By analyzing characteristic equations and using an iterative technique, a set of easily verifiable sufficient conditions are derived for the local and global stability of the nonnegative equilibria of the model. Numerical simulations are carried out to illustrate the validity of our results.

KW - Stage structure

KW - Time delay

KW - Characteristic equation

KW - Global stability

U2 - 10.1016/j.amc.2003.11.008

DO - 10.1016/j.amc.2003.11.008

M3 - Article

VL - 159

SP - 863

EP - 880

JO - Applied Mathematics and Computation

T2 - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

IS - 3

ER -