Pattern Formation in Predator-Prey Model with Delay and Cross Diffusion
We consider the effect of time delay and cross diffusion on the dynamics of a modified Leslie-Gower predator-prey model incorporating a prey refuge. Based on the stability analysis, we demonstrate that delayed feedback may generate Hopf and Turing instability under some conditions, resulting in spat...
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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/10.1155/2013/147232 |
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| _version_ | 1832564658448367616 |
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| author | Xinze Lian Shuling Yan Hailing Wang |
| author_facet | Xinze Lian Shuling Yan Hailing Wang |
| author_sort | Xinze Lian |
| collection | DOAJ |
| description | We consider the effect of time delay and cross diffusion on the dynamics of a modified Leslie-Gower predator-prey model incorporating a prey refuge. Based on the stability analysis, we demonstrate that delayed feedback may generate Hopf and Turing instability under some conditions, resulting in spatial patterns. One of the most interesting findings is that the model exhibits complex pattern replication: the model dynamics exhibits a delay and diffusion controlled formation growth not only to spots, stripes, and holes, but also to spiral pattern self-replication. The results indicate that time delay and cross diffusion play important roles in pattern formation. |
| format | Article |
| id | doaj-art-0aeabd8d1f6049048827bfd0fc8cafdb |
| 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-0aeabd8d1f6049048827bfd0fc8cafdb2025-02-03T01:10:24ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/147232147232Pattern Formation in Predator-Prey Model with Delay and Cross DiffusionXinze Lian0Shuling Yan1Hailing Wang2Department of Mathematics, Wenzhou University, Wenzhou 325035, ChinaCollege of Mathematics and Econometrics, Hunan University, Changsha 410082, ChinaDepartment of Mathematics, Hubei Minzu University, Enshi 445000, ChinaWe consider the effect of time delay and cross diffusion on the dynamics of a modified Leslie-Gower predator-prey model incorporating a prey refuge. Based on the stability analysis, we demonstrate that delayed feedback may generate Hopf and Turing instability under some conditions, resulting in spatial patterns. One of the most interesting findings is that the model exhibits complex pattern replication: the model dynamics exhibits a delay and diffusion controlled formation growth not only to spots, stripes, and holes, but also to spiral pattern self-replication. The results indicate that time delay and cross diffusion play important roles in pattern formation.http://dx.doi.org/10.1155/2013/147232 |
| spellingShingle | Xinze Lian Shuling Yan Hailing Wang Pattern Formation in Predator-Prey Model with Delay and Cross Diffusion Abstract and Applied Analysis |
| title | Pattern Formation in Predator-Prey Model with Delay and Cross Diffusion |
| title_full | Pattern Formation in Predator-Prey Model with Delay and Cross Diffusion |
| title_fullStr | Pattern Formation in Predator-Prey Model with Delay and Cross Diffusion |
| title_full_unstemmed | Pattern Formation in Predator-Prey Model with Delay and Cross Diffusion |
| title_short | Pattern Formation in Predator-Prey Model with Delay and Cross Diffusion |
| title_sort | pattern formation in predator prey model with delay and cross diffusion |
| url | http://dx.doi.org/10.1155/2013/147232 |
| work_keys_str_mv | AT xinzelian patternformationinpredatorpreymodelwithdelayandcrossdiffusion AT shulingyan patternformationinpredatorpreymodelwithdelayandcrossdiffusion AT hailingwang patternformationinpredatorpreymodelwithdelayandcrossdiffusion |