Global convergence of a reaction–diffusion predator–prey model with stage structure and nonlocal delays

Rui Xu; Fordyce Davidson; Mark Chaplain

doi:10.1016/j.camwa.2007.02.002

Global convergence of a reaction–diffusion predator–prey model with stage structure and nonlocal delays

Rui Xu (Lead / Corresponding author), Fordyce Davidson, Mark Chaplain

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

9 Citations (Scopus)

Abstract

In this paper, a Lotka–Volterra type reaction–diffusion predator–prey model with stage structure for the prey and nonlocal delays due to gestation of the predator is investigated. In the case of a general domain, sufficient conditions are obtained for the global convergence of positive solutions of the proposed problem by using the energy function method. Numerical simulations are carried out to illustrate the main results.

Original language	English
Pages (from-to)	770-788
Number of pages	19
Journal	Computers and Mathematics with Applications
Volume	53
Issue number	5
DOIs	https://doi.org/10.1016/j.camwa.2007.02.002
Publication status	Published - Mar 2007

Keywords

Stage structure
Reaction-diffusion
Nonlocal delay
Steady-state solution
Global convergence

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10.1016/j.camwa.2007.02.002

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title = "Global convergence of a reaction–diffusion predator–prey model with stage structure and nonlocal delays",

abstract = "In this paper, a Lotka–Volterra type reaction–diffusion predator–prey model with stage structure for the prey and nonlocal delays due to gestation of the predator is investigated. In the case of a general domain, sufficient conditions are obtained for the global convergence of positive solutions of the proposed problem by using the energy function method. Numerical simulations are carried out to illustrate the main results.",

keywords = "Stage structure, Reaction-diffusion, Nonlocal delay, Steady-state solution, Global convergence",

author = "Rui Xu and Fordyce Davidson and Mark Chaplain",

year = "2007",

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T1 - Global convergence of a reaction–diffusion predator–prey model with stage structure and nonlocal delays

AU - Xu, Rui

AU - Davidson, Fordyce

AU - Chaplain, Mark

PY - 2007/3

Y1 - 2007/3

N2 - In this paper, a Lotka–Volterra type reaction–diffusion predator–prey model with stage structure for the prey and nonlocal delays due to gestation of the predator is investigated. In the case of a general domain, sufficient conditions are obtained for the global convergence of positive solutions of the proposed problem by using the energy function method. Numerical simulations are carried out to illustrate the main results.

AB - In this paper, a Lotka–Volterra type reaction–diffusion predator–prey model with stage structure for the prey and nonlocal delays due to gestation of the predator is investigated. In the case of a general domain, sufficient conditions are obtained for the global convergence of positive solutions of the proposed problem by using the energy function method. Numerical simulations are carried out to illustrate the main results.

KW - Stage structure

KW - Reaction-diffusion

KW - Nonlocal delay

KW - Steady-state solution

KW - Global convergence

U2 - 10.1016/j.camwa.2007.02.002

DO - 10.1016/j.camwa.2007.02.002

M3 - Article

SN - 0898-1221

VL - 53

SP - 770

EP - 788

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 5

ER -

Global convergence of a reaction–diffusion predator–prey model with stage structure and nonlocal delays

Abstract

Keywords

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