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.
| Original language | English |
|---|---|
| Pages (from-to) | 137-150 |
| Number of pages | 14 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 328 |
| Issue number | 1 |
| DOIs | |
| State | Published - 1 Apr 2007 |
Keywords
- Asymptotic behavior
- Predator-prey model
- Reaction-diffusion system
- Time delay
- Upper and lower solutions