Open Access
2013 Complex Dynamics of a Diffusive Holling-Tanner Predator-Prey Model with the Allee Effect
Zongmin Yue, Xiaoqin Wang, Haifeng Liu
Abstr. Appl. Anal. 2013(SI08): 1-12 (2013). DOI: 10.1155/2013/270191


We investigate the complex dynamics of a diffusive Holling-Tanner predation model with the Allee effect on prey analytically and numerically. We examine the existence of the positive equilibria and the related dynamical behaviors of the model and find that when the model is with weak Allee effect, the solutions are local and global stability for some conditions around the positive equilibrium. In contrast, when the model is with strong Allee effect, this may lead to the phenomenon of bistability; that is to say, there is a separatrix curve that separates the behavior of trajectories of the system, implying that the model is highly sensitive to the initial conditions. Furthermore, we give the conditions of Turing instability and determine the Turing space in the parameters space. Based on these results, we perform a series of numerical simulations and find that the model exhibits complex pattern replication: spots, spots-stripes mixtures, and stripes patterns. The results show that the impact of the Allee effect essentially increases the models spatiotemporal complexity.


Download Citation

Zongmin Yue. Xiaoqin Wang. Haifeng Liu. "Complex Dynamics of a Diffusive Holling-Tanner Predator-Prey Model with the Allee Effect." Abstr. Appl. Anal. 2013 (SI08) 1 - 12, 2013.


Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 1267.37104
MathSciNet: MR3034907
Digital Object Identifier: 10.1155/2013/270191

Rights: Copyright © 2013 Hindawi

Vol.2013 • No. SI08 • 2013
Back to Top