Abstract and Applied Analysis

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

Wenzhen Gan, Canrong Tian, Qunying Zhang, and Zhigui Lin

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 936952, 14 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393449753

Digital Object Identifier
doi:10.1155/2013/936952

Mathematical Reviews number (MathSciNet)
MR3096817

Zentralblatt MATH identifier
07095511

Citation

Gan, Wenzhen; Tian, Canrong; Zhang, Qunying; Lin, Zhigui. Stability in a Simple Food Chain System with Michaelis-Menten Functional Response and Nonlocal Delays. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 936952, 14 pages. doi:10.1155/2013/936952. https://projecteuclid.org/euclid.aaa/1393449753


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