Electron. J. Diff. Eqns., Vol. 2005(2005), No. 131, pp. 1-11.

Asymptotic behavior of a predator-prey diffusion system with time delays

Yijie Meng, Yifu Wang

In this paper, we study a class of reaction-diffusion systems with time delays, which models the dynamics of predator-prey species. The global asymptotic convergence is established by the upper-lower solutions and iteration method in terms of the rate constants of the reaction function, independent of the time delays and the effect of diffusion.

Submitted September 12, 2005. Published November 24, 2005.
Math Subject Classifications: 35B40.
Key Words: Predator-prey diffusion system; asymptotic behavior; time delays; upper-lower solutions.

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Yijie Meng
Department of Mathematics, Xiang Fan University
Xiangfan, 441053, China
email: yijie_meng@sina.com
  Yifu Wang
Department of Applied Mathematics
Beijing Institute of Technology
Beijing, 100081, China
email: yifu_wang@163.com

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