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

Authors:
Rui Xu;M. A. J. Chaplain;F. A. Davidson
Affiliations:
Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, PR China and Department of Applied Mathematics, Yuncheng University, Yuncheng 044000, Shanxi, PR ...;Department of Mathematics, University of Dundee, Dundee DD1 4HN, UK;Department of Mathematics, University of Dundee, Dundee DD1 4HN, UK
Venue:
Computers & Mathematics with Applications
Year:
2007

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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.