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Complex Dynamics of a Diffusive Holling-Tanner Predator-Prey Model with the Allee Effect
Joint Authors
Wang, Xiaoqin
Yue, Zongmin
Liu, Haifeng
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-02-11
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Yue, Zongmin& Wang, Xiaoqin& Liu, Haifeng. 2013. Complex Dynamics of a Diffusive Holling-Tanner Predator-Prey Model with the Allee Effect. Abstract and Applied Analysis،Vol. 2013, no. 2013, pp.1-12.
https://search.emarefa.net/detail/BIM-459075
Modern Language Association (MLA)
Yue, Zongmin…[et al.]. Complex Dynamics of a Diffusive Holling-Tanner Predator-Prey Model with the Allee Effect. Abstract and Applied Analysis No. 2013 (2013), pp.1-12.
https://search.emarefa.net/detail/BIM-459075
American Medical Association (AMA)
Yue, Zongmin& Wang, Xiaoqin& Liu, Haifeng. Complex Dynamics of a Diffusive Holling-Tanner Predator-Prey Model with the Allee Effect. Abstract and Applied Analysis. 2013. Vol. 2013, no. 2013, pp.1-12.
https://search.emarefa.net/detail/BIM-459075
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-459075