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Asymptotic behavior of solutions for a class of predator-prey reaction-diffusion systems with time delays |
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| Authors: | Yuan-Ming Wang |
| Institution: | a Department of Mathematics, East China Normal University, Shanghai 200062, People's Republic of China11Corresponding address. b Division of Computational Science, E-Institute of Shanghai Universities, Shanghai Normal University, Shanghai 200234, People's Republic of China |
| Abstract: | The aim of this paper is to investigate the asymptotic behavior of solutions for a class of three-species predator-prey reaction-diffusion systems with time delays under homogeneous Neumann boundary condition. Some simple and easily verifiable conditions are given to the rate constants of the reaction functions to ensure the convergence of the time-dependent solution to a constant steady-state solution. The conditions for the convergence are independent of diffusion coefficients and time delays, and the conclusions are directly applicable to the corresponding parabolic-ordinary differential system and to the corresponding system without time delays. |
| Keywords: | Reaction-diffusion system Predator-prey model Time delay Asymptotic behavior Upper and lower solutions |
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