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

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 E∗ is stable. However, when time delay...

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Bibliographic Details
Main Authors: Boli Xie, Zhijun Wang, Yakui Xue, Zhenmin Zhang
Format: Article
Language:English
Published: Wiley 2015-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2015/102597
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Summary: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 E∗ is stable. However, when time delay is above the threshold value, the positive equilibrium E∗ 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.
ISSN:1026-0226
1607-887X