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

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...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2007-03, Vol.53 (5), p.770-788
Main Authors: Xu, Rui, Chaplain, M.A.J., Davidson, F.A.
Format: Article
Language:English
Subjects:
Computer simulation
Convergence
Delay
Energy use
Gestation
Global convergence
Mathematical analysis
Mathematical models
Nonlocal delay
Predators
Reaction–diffusion
Stage structure
Steady-state solution
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Summary: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.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2007.02.002