Pattern Formation in a Cross-Diffusive Ratio-Dependent Predator-Prey Model
This paper presents a theoretical analysis of evolutionary process that involves organisms distribution and their interaction of spatial distribution of the species with self- and cross-diffusion in a Holling-III ratio-dependent predator-prey model. The diffusion instability of the positive equilibr...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/814069 |
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| _version_ | 1832553402076233728 |
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| author | Xinze Lian Yanhong Yue Hailing Wang |
| author_facet | Xinze Lian Yanhong Yue Hailing Wang |
| author_sort | Xinze Lian |
| collection | DOAJ |
| description | This paper presents a theoretical analysis of evolutionary process that involves organisms distribution and their interaction of spatial distribution of the species with self- and cross-diffusion in a Holling-III ratio-dependent predator-prey model. The diffusion instability of the positive equilibrium of the model with Neumann boundary conditions is discussed. Furthermore, we present novel numerical evidence of time evolution of patterns controlled by self- and cross-diffusion in the model and find that the model dynamics exhibits a cross-diffusion controlled formation growth to spots, stripes, and spiral wave pattern replication, which show that reaction-diffusion model is useful to reveal the spatial predation dynamics in the real world. |
| format | Article |
| id | doaj-art-6b04e5695ae84903bc49899fafd7e13a |
| 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-6b04e5695ae84903bc49899fafd7e13a2025-02-03T05:54:05ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2012-01-01201210.1155/2012/814069814069Pattern Formation in a Cross-Diffusive Ratio-Dependent Predator-Prey ModelXinze Lian0Yanhong Yue1Hailing Wang2Chengdu Institute of Computer Application, Chinese Academy of Sciences, Chengdu 610041, ChinaSchool of Foreign Language, Wenzhou University, Wenzhou 325000, ChinaCollege of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Chongqing 400065, ChinaThis paper presents a theoretical analysis of evolutionary process that involves organisms distribution and their interaction of spatial distribution of the species with self- and cross-diffusion in a Holling-III ratio-dependent predator-prey model. The diffusion instability of the positive equilibrium of the model with Neumann boundary conditions is discussed. Furthermore, we present novel numerical evidence of time evolution of patterns controlled by self- and cross-diffusion in the model and find that the model dynamics exhibits a cross-diffusion controlled formation growth to spots, stripes, and spiral wave pattern replication, which show that reaction-diffusion model is useful to reveal the spatial predation dynamics in the real world.http://dx.doi.org/10.1155/2012/814069 |
| spellingShingle | Xinze Lian Yanhong Yue Hailing Wang Pattern Formation in a Cross-Diffusive Ratio-Dependent Predator-Prey Model Discrete Dynamics in Nature and Society |
| title | Pattern Formation in a Cross-Diffusive Ratio-Dependent Predator-Prey Model |
| title_full | Pattern Formation in a Cross-Diffusive Ratio-Dependent Predator-Prey Model |
| title_fullStr | Pattern Formation in a Cross-Diffusive Ratio-Dependent Predator-Prey Model |
| title_full_unstemmed | Pattern Formation in a Cross-Diffusive Ratio-Dependent Predator-Prey Model |
| title_short | Pattern Formation in a Cross-Diffusive Ratio-Dependent Predator-Prey Model |
| title_sort | pattern formation in a cross diffusive ratio dependent predator prey model |
| url | http://dx.doi.org/10.1155/2012/814069 |
| work_keys_str_mv | AT xinzelian patternformationinacrossdiffusiveratiodependentpredatorpreymodel AT yanhongyue patternformationinacrossdiffusiveratiodependentpredatorpreymodel AT hailingwang patternformationinacrossdiffusiveratiodependentpredatorpreymodel |