Turing Patterns in a Predator-Prey System with Self-Diffusion
For a predator-prey system, cross-diffusion has been confirmed to emerge Turing patterns. However, in the real world, the tendency for prey and predators moving along the direction of lower density of their own species, called self-diffusion, should be considered. For this, we investigate Turing in...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/891738 |
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| _version_ | 1832548873710600192 |
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| author | Hongwei Yin Xiaoyong Xiao Xiaoqing Wen |
| author_facet | Hongwei Yin Xiaoyong Xiao Xiaoqing Wen |
| author_sort | Hongwei Yin |
| collection | DOAJ |
| description | For a predator-prey system, cross-diffusion has been confirmed to emerge Turing patterns. However, in the real world, the tendency for prey and predators moving along the direction of lower density of their own species, called self-diffusion, should be considered. For this, we investigate Turing instability for a predator-prey system with nonlinear diffusion terms including the normal diffusion, cross-diffusion, and self-diffusion. A sufficient condition of Turing instability for this system is obtained by analyzing the linear stability of spatial homogeneous equilibrium state of this model. A series of numerical simulations reveal Turing parameter regions of the interaction of diffusion parameters. According to these regions, we further demonstrate dispersion relations and spatial patterns. Our results indicate that self-diffusion plays an important role in the spatial patterns. |
| format | Article |
| id | doaj-art-31a36245133143b8978c51f510a0c198 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-31a36245133143b8978c51f510a0c1982025-02-03T06:12:43ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/891738891738Turing Patterns in a Predator-Prey System with Self-DiffusionHongwei Yin0Xiaoyong Xiao1Xiaoqing Wen2School of Science, Nanchang University, Nanchang 330031, ChinaSchool of Science, Nanchang University, Nanchang 330031, ChinaSchool of Science, Nanchang University, Nanchang 330031, ChinaFor a predator-prey system, cross-diffusion has been confirmed to emerge Turing patterns. However, in the real world, the tendency for prey and predators moving along the direction of lower density of their own species, called self-diffusion, should be considered. For this, we investigate Turing instability for a predator-prey system with nonlinear diffusion terms including the normal diffusion, cross-diffusion, and self-diffusion. A sufficient condition of Turing instability for this system is obtained by analyzing the linear stability of spatial homogeneous equilibrium state of this model. A series of numerical simulations reveal Turing parameter regions of the interaction of diffusion parameters. According to these regions, we further demonstrate dispersion relations and spatial patterns. Our results indicate that self-diffusion plays an important role in the spatial patterns.http://dx.doi.org/10.1155/2013/891738 |
| spellingShingle | Hongwei Yin Xiaoyong Xiao Xiaoqing Wen Turing Patterns in a Predator-Prey System with Self-Diffusion Abstract and Applied Analysis |
| title | Turing Patterns in a Predator-Prey System with Self-Diffusion |
| title_full | Turing Patterns in a Predator-Prey System with Self-Diffusion |
| title_fullStr | Turing Patterns in a Predator-Prey System with Self-Diffusion |
| title_full_unstemmed | Turing Patterns in a Predator-Prey System with Self-Diffusion |
| title_short | Turing Patterns in a Predator-Prey System with Self-Diffusion |
| title_sort | turing patterns in a predator prey system with self diffusion |
| url | http://dx.doi.org/10.1155/2013/891738 |
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