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Discrete Dynamics in Nature and Society
Volume 2015, Article ID 102597, 8 pages
http://dx.doi.org/10.1155/2015/102597
Research Article

The Dynamics of a Delayed Predator-Prey Model with Double Allee Effect

1School of Mechatronic Engineering, North University of China, Taiyuan, Shanxi 030051, China
2Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, China

Received 30 June 2015; Accepted 27 July 2015

Academic Editor: Carlo Bianca

Copyright © 2015 Boli Xie 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

We study the dynamics of a delayed predator-prey model with double Allee effect. For the temporal model, we showed that there exists a threshold of time delay in predator-prey interactions; when time delay is below the threshold value, the positive equilibrium is stable. However, when time delay is above the threshold value, the positive equilibrium is unstable and period solution will emerge. For the spatiotemporal model, through numerical simulations, we show that the model dynamics exhibit rich parameter space Turing structures. The obtained results show that this system has rich dynamics; these patterns show that it is useful for a delayed predator-prey model with double Allee effect to reveal the spatial dynamics in the real model.