Pattern Formation in a Predator-Prey Model with Both Cross Diffusion and Time Delay
A predator-prey model with both cross diffusion and time delay is considered. We give the conditions for emerging Turing instability in detail. Furthermore, we illustrate the spatial patterns via numerical simulations, which show that the model dynamics exhibits a delay and diffusion controlled form...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/392435 |
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| _version_ | 1832559477197373440 |
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| author | Boli Xie Zhijun Wang Yakui Xue |
| author_facet | Boli Xie Zhijun Wang Yakui Xue |
| author_sort | Boli Xie |
| collection | DOAJ |
| description | A predator-prey model with both cross diffusion and time delay is considered. We give the conditions for emerging Turing instability in detail. Furthermore, we illustrate the spatial patterns via numerical simulations, which show that the model dynamics exhibits a delay and diffusion controlled formation growth not only of spots and stripe-like patterns, but also of the two coexist. The obtained results show that this system has rich dynamics; these patterns show that it is useful for the diffusive predation model with a delay effect to reveal the spatial dynamics in the real model. |
| format | Article |
| id | doaj-art-2c84d36e314944d6a2fde13be715d4f2 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-2c84d36e314944d6a2fde13be715d4f22025-02-03T01:29:57ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/392435392435Pattern Formation in a Predator-Prey Model with Both Cross Diffusion and Time DelayBoli Xie0Zhijun Wang1Yakui Xue2School of Mechatronic Engineering, North University of China, Taiyuan, Shan’xi 030051, ChinaSchool of Mechatronic Engineering, North University of China, Taiyuan, Shan’xi 030051, ChinaDepartment of Mathematics, North University of China, Taiyuan, Shan’xi 030051, ChinaA predator-prey model with both cross diffusion and time delay is considered. We give the conditions for emerging Turing instability in detail. Furthermore, we illustrate the spatial patterns via numerical simulations, which show that the model dynamics exhibits a delay and diffusion controlled formation growth not only of spots and stripe-like patterns, but also of the two coexist. The obtained results show that this system has rich dynamics; these patterns show that it is useful for the diffusive predation model with a delay effect to reveal the spatial dynamics in the real model.http://dx.doi.org/10.1155/2014/392435 |
| spellingShingle | Boli Xie Zhijun Wang Yakui Xue Pattern Formation in a Predator-Prey Model with Both Cross Diffusion and Time Delay Abstract and Applied Analysis |
| title | Pattern Formation in a Predator-Prey Model with Both Cross Diffusion and Time Delay |
| title_full | Pattern Formation in a Predator-Prey Model with Both Cross Diffusion and Time Delay |
| title_fullStr | Pattern Formation in a Predator-Prey Model with Both Cross Diffusion and Time Delay |
| title_full_unstemmed | Pattern Formation in a Predator-Prey Model with Both Cross Diffusion and Time Delay |
| title_short | Pattern Formation in a Predator-Prey Model with Both Cross Diffusion and Time Delay |
| title_sort | pattern formation in a predator prey model with both cross diffusion and time delay |
| url | http://dx.doi.org/10.1155/2014/392435 |
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