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Abstract and Applied Analysis
Volume 2013, Article ID 340980, 10 pages
http://dx.doi.org/10.1155/2013/340980
Research Article

Dynamical Analysis of a Stochastic Predator-Prey Model with an Allee Effect

College of Sciences, Nanjing University of Technology, Nanjing 211816, China

Received 23 July 2013; Revised 24 October 2013; Accepted 7 November 2013

Academic Editor: Chengjian Zhang

Copyright © 2013 Feng Rao. 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 present and analyze a modified Holling type-II predator-prey model that includes some important factors such as Allee effect, density-dependence, and environmental noise. By constructing suitable Lyapunov functions and applying Itô formula, some qualitative properties are given, such as the existence of global positive solutions, stochastic boundedness, and the global asymptotic stability. A series of numerical simulations to illustrate these mathematical findings are presented.