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Discrete Dynamics in Nature and Society
Volume 2014 (2014), Article ID 512817, 8 pages
http://dx.doi.org/10.1155/2014/512817
Research Article

Global Stability of a Stage-Structured Predator-Prey Model with Stochastic Perturbation

School of Mathematics Science, University of Electronic Science and Technology of China, Chengdu 611731, China

Received 14 October 2013; Accepted 4 January 2014; Published 24 February 2014

Academic Editor: Leonid Shaikhet

Copyright © 2014 Liu Yang and Shouming Zhong. 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 a new predator-prey model with stage structure on prey, in which the immature prey and the mature prey are preyed on by predator. We think that the model is more realistic and interesting than the one in which only the immature prey or the mature prey is consumed by predator. Our work shows that the stochastic model and its corresponding deterministic system have a unique global positive solution and the positive solution is global asymptotic stability for each model. If the positive equilibrium point of the deterministic system is globally stable, then the stochastic model will preserve the nice property provided that the noise is sufficiently small. Results are analyzed with the help of graphical illustrations.