Pattern Formation in a Semi-Ratio-Dependent Predator-Prey System with Diffusion
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...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2013/657286 |
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| author | Hunki Baek Dong Ick Jung Zhi-wen Wang |
| author_facet | Hunki Baek Dong Ick Jung Zhi-wen Wang |
| author_sort | Hunki Baek |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-e352ac1b5da44312b64a3f7f7730e45b |
| institution | OA Journals |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-e352ac1b5da44312b64a3f7f7730e45b2025-08-20T02:21:24ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2013-01-01201310.1155/2013/657286657286Pattern Formation in a Semi-Ratio-Dependent Predator-Prey System with DiffusionHunki Baek0Dong Ick Jung1Zhi-wen Wang2Department of Mathematics Education, Catholic University of Daegu, Gyeongsan, Gyeongbuk 712-702, Republic of KoreaDepartment of Mathematics, Kyungpook National University, Daegu 702-701, Republic of KoreaCollege of Mathematics and Computer, Ningxia University, Ningxia 750021, ChinaWe 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.http://dx.doi.org/10.1155/2013/657286 |
| spellingShingle | Hunki Baek Dong Ick Jung Zhi-wen Wang Pattern Formation in a Semi-Ratio-Dependent Predator-Prey System with Diffusion Discrete Dynamics in Nature and Society |
| title | Pattern Formation in a Semi-Ratio-Dependent Predator-Prey System with Diffusion |
| title_full | Pattern Formation in a Semi-Ratio-Dependent Predator-Prey System with Diffusion |
| title_fullStr | Pattern Formation in a Semi-Ratio-Dependent Predator-Prey System with Diffusion |
| title_full_unstemmed | Pattern Formation in a Semi-Ratio-Dependent Predator-Prey System with Diffusion |
| title_short | Pattern Formation in a Semi-Ratio-Dependent Predator-Prey System with Diffusion |
| title_sort | pattern formation in a semi ratio dependent predator prey system with diffusion |
| url | http://dx.doi.org/10.1155/2013/657286 |
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