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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 936952, 14 pages
http://dx.doi.org/10.1155/2013/936952
Research Article

Stability in a Simple Food Chain System with Michaelis-Menten Functional Response and Nonlocal Delays

1School of Mathematics and Physics, Jiangsu Teachers University of Technology, Changzhou 213001, China
2Basic Department, Yancheng Institute of Technology, Yangcheng 224003, China
3School of Mathematical Science, Yangzhou University, Yangzhou 225002, China

Received 26 April 2013; Accepted 8 July 2013

Academic Editor: Rodrigo Lopez Pouso

Copyright © 2013 Wenzhen Gan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper is concerned with the asymptotical behavior of solutions to the reaction-diffusion system under homogeneous Neumann boundary condition. By taking food ingestion and species' moving into account, the model is further coupled with Michaelis-Menten type functional response and nonlocal delay. Sufficient conditions are derived for the global stability of the positive steady state and the semitrivial steady state of the proposed problem by using the Lyapunov functional. Our results show that intraspecific competition benefits the coexistence of prey and predator. Furthermore, the introduction of Michaelis-Menten type functional response positively affects the coexistence of prey and predator, and the nonlocal delay is harmless for stabilities of all nonnegative steady states of the system. Numerical simulations are carried out to illustrate the main results.