**Persistence and global stability of a ratio-dependent predator-prey model with stage structure.** / Xu, Rui; Chaplain, M. A. J.; Davidson, F. A.

Research output: Contribution to journal › Article

Xu, R, Chaplain, MAJ & Davidson, FA 2004, 'Persistence and global stability of a ratio-dependent predator-prey model with stage structure' *Applied Mathematics and Computation*, vol 158, no. 3, pp. 729-744. DOI: 10.1016/j.amc.2003.10.012

Xu, R., Chaplain, M. A. J., & Davidson, F. A. (2004). Persistence and global stability of a ratio-dependent predator-prey model with stage structure. *Applied Mathematics and Computation*, *158*(3), 729-744. DOI: 10.1016/j.amc.2003.10.012

Xu R, Chaplain MAJ, Davidson FA. Persistence and global stability of a ratio-dependent predator-prey model with stage structure. Applied Mathematics and Computation. 2004 Nov;158(3):729-744. Available from, DOI: 10.1016/j.amc.2003.10.012

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title = "Persistence and global stability of a ratio-dependent predator-prey model with stage structure",

abstract = "A ratio-dependent predator–prey model with stage structure for prey is investigated. First, sufficient conditions are derived for the uniform persistence and impermanence of the model. Next, by constructing appropriate Lyapunov functions, a set of easily verifiable sufficient conditions are obtained for the global asymptotic stability of nonnegative equilibria of the model. Numerical simulations are presented to illustrate the validity of our main results.",

keywords = "Ratio-dependence, Predator-prey model, Stage structure, Uniform persistence, Global stability",

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

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year = "2004",

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journal = "Applied Mathematics and Computation",

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AU - Xu,Rui

AU - Chaplain,M. A. J.

AU - Davidson,F. A.

N1 - dc.publisher: Elsevier

PY - 2004/11

Y1 - 2004/11

N2 - A ratio-dependent predator–prey model with stage structure for prey is investigated. First, sufficient conditions are derived for the uniform persistence and impermanence of the model. Next, by constructing appropriate Lyapunov functions, a set of easily verifiable sufficient conditions are obtained for the global asymptotic stability of nonnegative equilibria of the model. Numerical simulations are presented to illustrate the validity of our main results.

AB - A ratio-dependent predator–prey model with stage structure for prey is investigated. First, sufficient conditions are derived for the uniform persistence and impermanence of the model. Next, by constructing appropriate Lyapunov functions, a set of easily verifiable sufficient conditions are obtained for the global asymptotic stability of nonnegative equilibria of the model. Numerical simulations are presented to illustrate the validity of our main results.

KW - Ratio-dependence

KW - Predator-prey model

KW - Stage structure

KW - Uniform persistence

KW - Global stability

U2 - 10.1016/j.amc.2003.10.012

DO - 10.1016/j.amc.2003.10.012

M3 - Article

VL - 158

SP - 729

EP - 744

JO - Applied Mathematics and Computation

T2 - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

IS - 3

ER -