Cross-Diffusion-Driven Instability in a Reaction-Diffusion Harrison Predator-Prey Model
We present a theoretical analysis of processes of pattern formation that involves organisms distribution and their interaction of spatially distributed population with cross-diffusion in a Harrison-type predator-prey model. We analyze the global behaviour of the model by establishing a Lyapunov func...
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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/10.1155/2013/306467 |
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| _version_ | 1832565159752630272 |
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| author | Xiaoqin Wang Yongli Cai |
| author_facet | Xiaoqin Wang Yongli Cai |
| author_sort | Xiaoqin Wang |
| collection | DOAJ |
| description | We present a theoretical analysis of processes of pattern formation that involves organisms distribution and their interaction of spatially distributed population with cross-diffusion in a Harrison-type predator-prey model. We analyze the global behaviour of the model by establishing a Lyapunov function. We carry out the analytical study in detail and find out the certain conditions for Turing’s instability induced by cross-diffusion. And the numerical results reveal that, on increasing the value of the half capturing saturation constant, the sequences “spots → spot-stripe mixtures → stripes → hole-stripe mixtures → holes” are observed. The results show that the model dynamics exhibits complex pattern replication controlled by the cross-diffusion. |
| format | Article |
| id | doaj-art-43e212d58c7749a38046903002c02a8b |
| 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-43e212d58c7749a38046903002c02a8b2025-02-03T01:09:05ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/306467306467Cross-Diffusion-Driven Instability in a Reaction-Diffusion Harrison Predator-Prey ModelXiaoqin Wang0Yongli Cai1Faculty of Science, Shaanxi University of Science and Technology, Xi’an 710021, ChinaSchool of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou 510275, ChinaWe present a theoretical analysis of processes of pattern formation that involves organisms distribution and their interaction of spatially distributed population with cross-diffusion in a Harrison-type predator-prey model. We analyze the global behaviour of the model by establishing a Lyapunov function. We carry out the analytical study in detail and find out the certain conditions for Turing’s instability induced by cross-diffusion. And the numerical results reveal that, on increasing the value of the half capturing saturation constant, the sequences “spots → spot-stripe mixtures → stripes → hole-stripe mixtures → holes” are observed. The results show that the model dynamics exhibits complex pattern replication controlled by the cross-diffusion.http://dx.doi.org/10.1155/2013/306467 |
| spellingShingle | Xiaoqin Wang Yongli Cai Cross-Diffusion-Driven Instability in a Reaction-Diffusion Harrison Predator-Prey Model Abstract and Applied Analysis |
| title | Cross-Diffusion-Driven Instability in a Reaction-Diffusion Harrison Predator-Prey Model |
| title_full | Cross-Diffusion-Driven Instability in a Reaction-Diffusion Harrison Predator-Prey Model |
| title_fullStr | Cross-Diffusion-Driven Instability in a Reaction-Diffusion Harrison Predator-Prey Model |
| title_full_unstemmed | Cross-Diffusion-Driven Instability in a Reaction-Diffusion Harrison Predator-Prey Model |
| title_short | Cross-Diffusion-Driven Instability in a Reaction-Diffusion Harrison Predator-Prey Model |
| title_sort | cross diffusion driven instability in a reaction diffusion harrison predator prey model |
| url | http://dx.doi.org/10.1155/2013/306467 |
| work_keys_str_mv | AT xiaoqinwang crossdiffusiondriveninstabilityinareactiondiffusionharrisonpredatorpreymodel AT yonglicai crossdiffusiondriveninstabilityinareactiondiffusionharrisonpredatorpreymodel |