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An allelopathic competition model with quorum sensing and delayed toxicant production

Paolo Fergola Marianna Cerasuolo Edoardo Beretta

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MBE2006,1,37doi:10.3934/mbe.2006.3.37

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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