The Dynamics of a Delayed Predator-Prey Model with Double Allee Effect. (4th October 2015)

• Record Type: Journal Article
• Authors: Xie, Boli; Wang, Zhijun; Xue, Yakui; Zhang, Zhenmin
• Other Names: Bianca Carlo Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2015(2015)
• Publication Date: 2015-10-04
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2015/102597
• Languages: English
• ISSNs: 1026-0226

Abstract

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 equilibriumE ∗ is stable. However, when time delay is above the threshold value, the positive equilibriumE ∗ 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.