American Institute of Mathematical Sciences

Advanced
2006, 3(1): 37-50. doi: 10.3934/mbe.2006.3.37

An allelopathic competition model with quorum sensing and delayed toxicant production

Paolo Fergola 1, , Marianna Cerasuolo 1, and  Edoardo Beretta 2,

1. 

Dipartimento di Matematica e Applicazioni ''R. Caccioppoli", Università degli Studi di Napoli Federico II, Complesso di Monte S. Angelo, Via Cintia, 80126 Napoli, Italy, Italy
2. 

Istituto di Biomatematica, Università degli Studi di Urbino, Località Crocicchia, I-61029 Urbino, Italy

Received  January 2005 Revised  April 2005 Published  November 2005

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.
Keywords: distributed delay, global stability., allelopathy, chemostat models, quorum sensing.
Mathematics Subject Classification: 93D20,34D20,34D23,92B0.
Citation: Paolo Fergola, Marianna Cerasuolo, Edoardo Beretta. An allelopathic competition model with quorum sensing and delayed toxicant production. Mathematical Biosciences & Engineering, 2006, 3 (1) : 37-50. doi: 10.3934/mbe.2006.3.37
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