Abstract and Applied Analysis
Volume 2014, Article ID 426702, 11 pages
http://dx.doi.org/10.1155/2014/426702
Dynamical Behavior of a Stochastic Food-Chain System with Beddington-DeAngelis Functional Response
College of Information Technology, Shanghai Ocean University, Shanghai 201306, China
Received 11 March 2014; Revised 13 May 2014; Accepted 18 May 2014; Published 11 June 2014
Academic Editor: Yongli Song
Copyright © 2014 Yanming Ge and Zigen Song. 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
We investigate a stochastic Food-Chain System , , , where , = is a standard Brownian motion. Firstly, the existence, the uniqueness, and the positivity of the solution are proved. Secondly, the stochastically ultimate boundedness of the system is investigated. Thirdly, the boundedness of moments and upper-growth rate of the solution are obtained. Then the global attractivity of the system is discussed. Finally, the main results are illustrated by several examples.