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Spatiotemporal Pattern in a Self- and Cross-Diffusive Predation Model with the Allee Effect
Author
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-07-01
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
This paper proposes and analyzes a mathematical model for a predator-prey interaction with the Allee effect on prey species and with self- and cross-diffusion.
The effect of diffusion which can drive the model with zero-flux boundary conditions to Turing instability is investigated.
We present numerical evidence of time evolution of patterns controlled by self- and cross-diffusion in the model and find that the model dynamics exhibits a cross-diffusion controlled formation growth to spotted and striped-like coexisting and spotted pattern replication.
Moreover, we discuss the effect of cross-diffusivity on the stability of the nontrivial equilibrium of the model, which depends upon the magnitudes of the self- and cross-diffusion coefficients.
The obtained results show that cross-diffusion plays an important role in the pattern formation of the predator-prey model.
It is also useful to apply the reaction-diffusion model to reveal the spatial predation in the real world.
American Psychological Association (APA)
Rao, Feng. 2013. Spatiotemporal Pattern in a Self- and Cross-Diffusive Predation Model with the Allee Effect. Discrete Dynamics in Nature and Society،Vol. 2013, no. 2013, pp.1-9.
https://search.emarefa.net/detail/BIM-490090
Modern Language Association (MLA)
Rao, Feng. Spatiotemporal Pattern in a Self- and Cross-Diffusive Predation Model with the Allee Effect. Discrete Dynamics in Nature and Society No. 2013 (2013), pp.1-9.
https://search.emarefa.net/detail/BIM-490090
American Medical Association (AMA)
Rao, Feng. Spatiotemporal Pattern in a Self- and Cross-Diffusive Predation Model with the Allee Effect. Discrete Dynamics in Nature and Society. 2013. Vol. 2013, no. 2013, pp.1-9.
https://search.emarefa.net/detail/BIM-490090
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-490090