An allelopathic competition model with quorum sensing and delayed toxicant production

  • 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.

    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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  • 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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    © 2006 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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