Pattern Formation in a Semi-Ratio-Dependent Predator-Prey System with Diffusion
Joint Authors
Jung, Dong Ick
Baek, Hunki
Wang, Zhi-wen
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-04-04
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
We investigate spatiotemporal dynamics of a semi-ratio-dependent predator-prey system with reaction-diffusion and zero-flux boundary.
We obtain the conditions for Hopf, Turing, and wave bifurcations of the system in a spatial domain by making use of the linear stability analysis and the bifurcation analysis.
In addition, for an initial condition which is a small amplitude random perturbation around the steady state, we classify spatial pattern formations of the system by using numerical simulations.
The results of numerical simulations unveil that there are various spatiotemporal patterns including typical Turing patterns such as spotted, spot-stripelike mixtures and stripelike patterns thanks to the Turing instability, that an oscillatory wave pattern can be emerged due to the Hopf and wave instability, and that cooperations of Turing and Hopf instabilities can cause occurrence of spiral patterns instead of typical Turing patterns.
Finally, we discuss spatiotemporal dynamics of the system for several different asymmetric initial conditions via numerical simulations.
American Psychological Association (APA)
Baek, Hunki& Jung, Dong Ick& Wang, Zhi-wen. 2013. Pattern Formation in a Semi-Ratio-Dependent Predator-Prey System with Diffusion. Discrete Dynamics in Nature and Society،Vol. 2013, no. 2013, pp.1-14.
https://search.emarefa.net/detail/BIM-488783
Modern Language Association (MLA)
Baek, Hunki…[et al.]. Pattern Formation in a Semi-Ratio-Dependent Predator-Prey System with Diffusion. Discrete Dynamics in Nature and Society No. 2013 (2013), pp.1-14.
https://search.emarefa.net/detail/BIM-488783
American Medical Association (AMA)
Baek, Hunki& Jung, Dong Ick& Wang, Zhi-wen. Pattern Formation in a Semi-Ratio-Dependent Predator-Prey System with Diffusion. Discrete Dynamics in Nature and Society. 2013. Vol. 2013, no. 2013, pp.1-14.
https://search.emarefa.net/detail/BIM-488783
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-488783