Mathematical Biosciences and Engineering (Oct 2005)

An allelopathic competition model with quorum sensing and delayed toxicant production

  • Paolo Fergola,
  • Marianna Cerasuolo,
  • Edoardo Beretta

DOI
https://doi.org/10.3934/mbe.2006.3.37
Journal volume & issue
Vol. 3, no. 1
pp. 37 – 50

Abstract

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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.

Keywords