Pattern Formation in a Cross-Diffusive Holling-Tanner Model
We present a theoretical analysis of the processes of pattern formation that involves organisms distribution and their interaction of spatially distributed population with self- as well as cross-diffusion in a Holling-Tanner predator-prey model; the sufficient conditions for the Turing instability w...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/828219 |
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| _version_ | 1832545493098430464 |
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| author | Weiming Wang Zhengguang Guo R. K. Upadhyay Yezhi Lin |
| author_facet | Weiming Wang Zhengguang Guo R. K. Upadhyay Yezhi Lin |
| author_sort | Weiming Wang |
| collection | DOAJ |
| description | We present a theoretical analysis of the processes of pattern formation that involves organisms distribution and their interaction of spatially distributed population with self- as well as cross-diffusion in a Holling-Tanner predator-prey model; the sufficient conditions for the Turing instability with zero-flux boundary conditions are obtained; Hopf and Turing bifurcation in a spatial domain is presented, too. Furthermore, we present novel numerical evidence of time evolution of patterns controlled by self- as well as cross-diffusion in the model, and find that the model dynamics exhibits a cross-diffusion controlled formation growth not only to spots, but also to strips, holes, and stripes-spots replication. And the methods and results in the present paper may be useful for the research of the pattern formation in the cross-diffusive model. |
| format | Article |
| id | doaj-art-31ba3127a5b74c16ad95282923995562 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-31ba3127a5b74c16ad952829239955622025-02-03T07:25:29ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2012-01-01201210.1155/2012/828219828219Pattern Formation in a Cross-Diffusive Holling-Tanner ModelWeiming Wang0Zhengguang Guo1R. K. Upadhyay2Yezhi Lin3College of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang 325035, ChinaCollege of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang 325035, ChinaDepartment of Applied Mathematics, Indian School of Mines, Dhanbad, Jharkhand 826004, IndiaCollege of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang 325035, ChinaWe present a theoretical analysis of the processes of pattern formation that involves organisms distribution and their interaction of spatially distributed population with self- as well as cross-diffusion in a Holling-Tanner predator-prey model; the sufficient conditions for the Turing instability with zero-flux boundary conditions are obtained; Hopf and Turing bifurcation in a spatial domain is presented, too. Furthermore, we present novel numerical evidence of time evolution of patterns controlled by self- as well as cross-diffusion in the model, and find that the model dynamics exhibits a cross-diffusion controlled formation growth not only to spots, but also to strips, holes, and stripes-spots replication. And the methods and results in the present paper may be useful for the research of the pattern formation in the cross-diffusive model.http://dx.doi.org/10.1155/2012/828219 |
| spellingShingle | Weiming Wang Zhengguang Guo R. K. Upadhyay Yezhi Lin Pattern Formation in a Cross-Diffusive Holling-Tanner Model Discrete Dynamics in Nature and Society |
| title | Pattern Formation in a Cross-Diffusive Holling-Tanner Model |
| title_full | Pattern Formation in a Cross-Diffusive Holling-Tanner Model |
| title_fullStr | Pattern Formation in a Cross-Diffusive Holling-Tanner Model |
| title_full_unstemmed | Pattern Formation in a Cross-Diffusive Holling-Tanner Model |
| title_short | Pattern Formation in a Cross-Diffusive Holling-Tanner Model |
| title_sort | pattern formation in a cross diffusive holling tanner model |
| url | http://dx.doi.org/10.1155/2012/828219 |
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