An allelopathic competition model with quorum sensing and delayed toxicant production

Paolo Fergola; Marianna Cerasuolo; Edoardo Beretta; Paolo Fergola; Marianna Cerasuolo; Edoardo Beretta

doi:10.3934/mbe.2006.3.37

Mathematical Biosciences and Engineering

2006, Volume 3, Issue 1: 37-50. doi: 10.3934/mbe.2006.3.37

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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

Received: 01 January 2005 Accepted: 29 June 2018 Published: 01 November 2005
MSC : 93D20,34D20,34D23,92B05.

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.
- 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[J]. Mathematical Biosciences and Engineering, 2006, 3(1): 37-50. doi: 10.3934/mbe.2006.3.37

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Abstract

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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