Asymptotic behavior of solutions for a cooperation-diffusion model with a saturating interaction

Authors:
Yuan-Ming Wang
Affiliations:
Department of Mathematics East China Normal University Shanghai 200062, P.R. China and Division of Computational Science E-Institute of Shanghai Universities Shanghai Normal University Shanghai 20 ...
Venue:
Computers & Mathematics with Applications
Year:
2006

Citing 2
Cited 1

Necessary and sufficient condition for the existence of positive solutions of certain cooperative system

Nonlinear Analysis: Theory, Methods & Applications
Convergence of solutions of reaction-diffusion systems with time delays

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Asymptotic behavior of solutions for a Lotka-Volterra mutualism reaction-diffusion system with time delays

Computers & Mathematics with Applications

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Abstract

This paper is concerned with a Lotka-Volterra cooperation-diffusion model with a saturating interaction term for one species. The goal of the paper is to investigate the asymptotic behavior of the time- dependent solution in relation to the corresponding steady-state solutions under homogeneous Neumann boundary condition. Some simple and easily verifiable conditions are given to the rate constants so that for every nontrivial nonnegative initial function the corresponding time-dependent solution converges to one of the nonnegative constant steady-state solutions as time tends to infinity. This convergence result leads to the existence and uniqueness of a positive (or nonnegative) steady-state solution and the global asymptotic stability of a given nonnegative constant steady-state solution. In terms of ecological dynamics, it also gives some coexistence, permanence and extinction results for the model.