Global convergence of a predator-prey model with stage structure and spatio-temporal delay

Rui Xu

doi:10.3934/dcdsb.2011.15.273

Article Contents

2011, Volume 15, Issue 1: 273-291. Doi: 10.3934/dcdsb.2011.15.273

This issue Previous Article A rigorous derivation of hemitropy in nonlinearly elastic rods Next Article Feedback stabilization methods for the numerical solution of ordinary differential equations

Global convergence of a predator-prey model with stage structure and spatio-temporal delay

Rui Xu^1,

1.
Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003

Received: May 2009

Revised: February 2010

Published online: October 2010

Abstract / Introduction Related Papers Cited by

Abstract

In this paper, a predator-prey model with stage structure for the predator and a spatio-temporal delay describing the gestation period of the predator under homogeneous Neumann boundary conditions is investigated. By analyzing the corresponding characteristic equations, the local stability of a positive steady state and each of boundary steady states is established. Sufficient conditions are derived for the global attractiveness of the positive steady state and the global stability of the semi-trivial steady state of the proposed problem by using the method of upper-lower solutions and its associated monotone iteration scheme. Numerical simulations are carried out to illustrate the main results.

Keywords:

Mathematics Subject Classification: Primary: 35B35, 35K57; Secondary: 92D25.

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