Turing patterns in a networked vegetation model
A vegetation model composed of water and plants was proposed by introducing a weighted graph Laplacian operator into the reaction-diffusion dynamics. We showed the global existence and uniqueness of the solution via monotone iterative sequence. The parameter space of Turing patterns for plant behavi...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-11-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2024334 |
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| _version_ | 1832590825841754112 |
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| author | Xiaomei Bao Canrong Tian |
| author_facet | Xiaomei Bao Canrong Tian |
| author_sort | Xiaomei Bao |
| collection | DOAJ |
| description | A vegetation model composed of water and plants was proposed by introducing a weighted graph Laplacian operator into the reaction-diffusion dynamics. We showed the global existence and uniqueness of the solution via monotone iterative sequence. The parameter space of Turing patterns for plant behavior is obtained based on the analysis of the eigenvalues of the Laplacian of weighted graph, while the amplitude equation determining the stability of Turing patterns is obtained by weakly nonlinear analysis. We also show that the optimal rainfall is only determined by the density of the water. By some numerical simulations, we examine the individual effect of diffusion term on the formation of regular Turing patterns. We show that the large diffusion induces stable Turing patterns. |
| format | Article |
| id | doaj-art-8766bc843426404daa35a9fdaeb6e645 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-8766bc843426404daa35a9fdaeb6e6452025-01-23T07:48:07ZengAIMS PressMathematical Biosciences and Engineering1551-00182024-11-0121117601762010.3934/mbe.2024334Turing patterns in a networked vegetation modelXiaomei Bao0Canrong Tian1School of Foreign Languages, Yancheng Institute of Technology, Yancheng 224003, ChinaSchool of Mathematics and Physics, Yancheng Institute of Technology, Yancheng 224003, ChinaA vegetation model composed of water and plants was proposed by introducing a weighted graph Laplacian operator into the reaction-diffusion dynamics. We showed the global existence and uniqueness of the solution via monotone iterative sequence. The parameter space of Turing patterns for plant behavior is obtained based on the analysis of the eigenvalues of the Laplacian of weighted graph, while the amplitude equation determining the stability of Turing patterns is obtained by weakly nonlinear analysis. We also show that the optimal rainfall is only determined by the density of the water. By some numerical simulations, we examine the individual effect of diffusion term on the formation of regular Turing patterns. We show that the large diffusion induces stable Turing patterns.https://www.aimspress.com/article/doi/10.3934/mbe.2024334networked vegetation modelturing patterngraph laplaceamplitude equationoptimal control |
| spellingShingle | Xiaomei Bao Canrong Tian Turing patterns in a networked vegetation model Mathematical Biosciences and Engineering networked vegetation model turing pattern graph laplace amplitude equation optimal control |
| title | Turing patterns in a networked vegetation model |
| title_full | Turing patterns in a networked vegetation model |
| title_fullStr | Turing patterns in a networked vegetation model |
| title_full_unstemmed | Turing patterns in a networked vegetation model |
| title_short | Turing patterns in a networked vegetation model |
| title_sort | turing patterns in a networked vegetation model |
| topic | networked vegetation model turing pattern graph laplace amplitude equation optimal control |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2024334 |
| work_keys_str_mv | AT xiaomeibao turingpatternsinanetworkedvegetationmodel AT canrongtian turingpatternsinanetworkedvegetationmodel |