An allelopathic competition model with quorum sensing and delayed toxicant production
The dynamics of a differential functional equation system representing an allelopathic competition is analyzed. The delayed allelochemical production process is represented by means of a distributed delay term in a linear quorum-sensing model. Sufficient conditions for local asymptotic stability pro...
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| Format: | Article |
| Language: | English |
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AIMS Press
2005-10-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.37 |
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| _version_ | 1832590272869957632 |
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| author | Paolo Fergola Marianna Cerasuolo Edoardo Beretta |
| author_facet | Paolo Fergola Marianna Cerasuolo Edoardo Beretta |
| author_sort | Paolo Fergola |
| collection | DOAJ |
| description | The dynamics of a differential functional equation system representing an allelopathic competition is analyzed. The delayed allelochemical production process is represented by means of a distributed delay term in a linear quorum-sensing model. Sufficient conditions for local asymptotic stability properties of biologically meaningful steady-state solutions are given in terms of the parameters of the system. A global asymptotic stability result is also proved by constructing a suitable Lyapunov functional. Some simulations confirm the analytical results. |
| format | Article |
| id | doaj-art-9c0d6c52680d44e186c0ef36956ad188 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2005-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-9c0d6c52680d44e186c0ef36956ad1882025-01-24T01:51:11ZengAIMS PressMathematical Biosciences and Engineering1551-00182005-10-0131375010.3934/mbe.2006.3.37An allelopathic competition model with quorum sensing and delayed toxicant productionPaolo Fergola0Marianna Cerasuolo1Edoardo Beretta2Dipartimento di Matematica e Applicazioni ''R. Caccioppoli", Università degli Studi di Napoli Federico II, Complesso di Monte S. Angelo, Via Cintia, 80126 NapoliDipartimento di Matematica e Applicazioni ''R. Caccioppoli", Università degli Studi di Napoli Federico II, Complesso di Monte S. Angelo, Via Cintia, 80126 NapoliIstituto di Biomatematica, Università degli Studi di Urbino, Località Crocicchia, I-61029 UrbinoThe dynamics of a differential functional equation system representing an allelopathic competition is analyzed. The delayed allelochemical production process is represented by means of a distributed delay term in a linear quorum-sensing model. Sufficient conditions for local asymptotic stability properties of biologically meaningful steady-state solutions are given in terms of the parameters of the system. A global asymptotic stability result is also proved by constructing a suitable Lyapunov functional. Some simulations confirm the analytical results.https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.37distributed delayglobal stability.allelopathychemostat modelsquorum sensing |
| spellingShingle | Paolo Fergola Marianna Cerasuolo Edoardo Beretta An allelopathic competition model with quorum sensing and delayed toxicant production Mathematical Biosciences and Engineering distributed delay global stability. allelopathy chemostat models quorum sensing |
| title | An allelopathic competition model with quorum sensing and delayed toxicant production |
| title_full | An allelopathic competition model with quorum sensing and delayed toxicant production |
| title_fullStr | An allelopathic competition model with quorum sensing and delayed toxicant production |
| title_full_unstemmed | An allelopathic competition model with quorum sensing and delayed toxicant production |
| title_short | An allelopathic competition model with quorum sensing and delayed toxicant production |
| title_sort | allelopathic competition model with quorum sensing and delayed toxicant production |
| topic | distributed delay global stability. allelopathy chemostat models quorum sensing |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.37 |
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