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An allelopathic competition model with quorum sensing and delayed toxicant production

1. Dipartimento di Matematica e Applicazioni ''R. Caccioppoli", Università degli Studi di Napoli Federico II, Complesso di Monte S. Angelo, Via Cintia, 80126 Napoli
2. Istituto di Biomatematica, Università degli Studi di Urbino, Località Crocicchia, I-61029 Urbino

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.
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Keywords distributed delay; global stability.; allelopathy; chemostat models; quorum sensing

Citation: Paolo Fergola, Marianna Cerasuolo, Edoardo Beretta. An allelopathic competition model with quorum sensing and delayed toxicant production. Mathematical Biosciences and Engineering, 2006, 3(1): 37-50. doi: 10.3934/mbe.2006.3.37


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Copyright Info: 2006, Paolo Fergola, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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