title: An allelopathic competition model with quorum sensing and delayed toxicant production.
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.
authors.affiliation: Dipartimento di Matematica e Applicazioni "R. Caccioppoli" Universita degli Studi di Napoli Federico II Complesso di Monte S. Angelo, Via Cintia, 80126 Napoli, Italy. paolo.fergola@dma.unina.it.
authors.forename: Paolo
authors.initials: P
authors.lastname: Fergola
authors.forename: Marianna
authors.initials: M
authors.lastname: Cerasuolo
authors.forename: Edoardo
authors.initials: E
authors.lastname: Beretta