A note on the replicator equation with explicit space and global regulation
A replicator equation with explicit space and global regulation is considered. This model provides a naturalframework to follow frequencies of species that are distributed in the space. For this model, analogues to classical notions of the Nash equilibrium and evolutionary stable state are provided....
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| Format: | Article |
| Language: | English |
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AIMS Press
2011-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.659 |
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| author | Alexander S. Bratus Vladimir P. Posvyanskii Artem S. Novozhilov |
| author_facet | Alexander S. Bratus Vladimir P. Posvyanskii Artem S. Novozhilov |
| author_sort | Alexander S. Bratus |
| collection | DOAJ |
| description | A replicator equation with explicit space and global regulation is considered. This model provides a naturalframework to follow frequencies of species that are distributed in the space. For this model, analogues to classical notions of the Nash equilibrium and evolutionary stable state are provided. A sufficient condition for a uniform stationary state to be a spatially distributed evolutionary stable state is presented and illustrated with examples. |
| format | Article |
| id | doaj-art-26b33a3e1319407791d168118373e4d6 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2011-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-26b33a3e1319407791d168118373e4d62025-01-24T02:01:59ZengAIMS PressMathematical Biosciences and Engineering1551-00182011-05-018365967610.3934/mbe.2011.8.659A note on the replicator equation with explicit space and global regulationAlexander S. Bratus0Vladimir P. Posvyanskii1Artem S. Novozhilov2Applied Mathematics–1, Moscow State University of Railway Engineering, Obraztsova 9, Moscow, 127994Applied Mathematics–1, Moscow State University of Railway Engineering, Obraztsova 9, Moscow, 127994Applied Mathematics–1, Moscow State University of Railway Engineering, Obraztsova 9, Moscow, 127994A replicator equation with explicit space and global regulation is considered. This model provides a naturalframework to follow frequencies of species that are distributed in the space. For this model, analogues to classical notions of the Nash equilibrium and evolutionary stable state are provided. A sufficient condition for a uniform stationary state to be a spatially distributed evolutionary stable state is presented and illustrated with examples.https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.659evolutionary stable statereaction-diffusion systems.nash equilibriumreplicator equation |
| spellingShingle | Alexander S. Bratus Vladimir P. Posvyanskii Artem S. Novozhilov A note on the replicator equation with explicit space and global regulation Mathematical Biosciences and Engineering evolutionary stable state reaction-diffusion systems. nash equilibrium replicator equation |
| title | A note on the replicator equation with explicit space and global regulation |
| title_full | A note on the replicator equation with explicit space and global regulation |
| title_fullStr | A note on the replicator equation with explicit space and global regulation |
| title_full_unstemmed | A note on the replicator equation with explicit space and global regulation |
| title_short | A note on the replicator equation with explicit space and global regulation |
| title_sort | note on the replicator equation with explicit space and global regulation |
| topic | evolutionary stable state reaction-diffusion systems. nash equilibrium replicator equation |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.659 |
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