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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 973805, 10 pages
http://dx.doi.org/10.1155/2013/973805
Research Article

Asymmetrical Impact of Allee Effect on a Discrete-Time Predator-Prey System

School of Mathematics and Computer Science, Northwest University for Nationalities, Lanzhou 730030, China

Received 28 August 2012; Revised 2 March 2013; Accepted 8 March 2013

Academic Editor: Vu Phat

Copyright © 2013 Wenting Wang 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

A discrete-time predator-prey model is proposed with Leslie-type numerical response, and the asymmetrical influence of Allee effect on the proposed system is investigated. By mathematical analysis, locally stable conditions for the equilibrium points of the considered systems with or without Allee effect are obtained firstly. Furthermore, numerical simulation is used to verify the results and detect some new outcomes. The results show that Allee effect on predator leads the system to its stable state in much longer time. Conversely, the prey population with Allee effect makes it much faster. In particular, a large value of Allee effect on prey results in periodic dynamics of the system.