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Mathematical Biosciences and Engineering

2006, Volume 3, Issue 1: 37-50. doi: 10.3934/mbe.2006.3.37
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An allelopathic competition model with quorum sensing and delayed toxicant production

  • 1.
    Dipartimento di Matematica e Applicazioni ''R. Caccioppoli", Università degli Studi di Napoli Federico II, Complesso di Monte S. Angelo, Via Cintia, 80126 Napoli
  • 2.
    Istituto di Biomatematica, Università degli Studi di Urbino, Località Crocicchia, I-61029 Urbino
  • 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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    2. P. FERGOLA, WENDI WANG, ON THE INFLUENCES OF DEFENSIVE VOLATILES OF PLANTS IN TRITROPHIC INTERACTIONS, 2011, 19, 0218-3390, 345, 10.1142/S0218339011004044
    3. Zhang Zhonghua, Suo Yaohong, Zhang Juan, Peng Jigeng, A bacteria-immunity system with delayed quorum sensing, 2009, 30, 1598-5865, 201, 10.1007/s12190-008-0167-8
    4. Zhang Juan, Zhang Zhonghua, Suo Yaohong, Hopf bifurcation of a bacteria-immunity system with delayed quorum sensing, 2010, 215, 00963003, 3936, 10.1016/j.amc.2009.11.042
    5. Marina DellaGreca, Armando Zarrelli, Paolo Fergola, Marianna Cerasuolo, Antonino Pollio, Gabriele Pinto, Fatty Acids Released by Chlorella vulgaris and Their Role in Interference with Pseudokirchneriella subcapitata: Experiments and Modelling, 2010, 36, 0098-0331, 339, 10.1007/s10886-010-9753-y
    6. Paolo Fergola, Jianquan Li, Zhien Ma, On the dynamical behavior of some algal allelopathic competitions in chemostat-like environment, 2011, 60, 0035-5038, 313, 10.1007/s11587-011-0108-y
    7. Jeet Banerjee, Ritwik Kumar Layek, Sourav K. Sasmal, Dibakar Ghosh, Delayed evolutionary model for public goods competition with policing in phenotypically variant bacterial biofilms, 2019, 126, 1286-4854, 18002, 10.1209/0295-5075/126/18002
    8. P. Fergola, M. Cerasuolo, A. Pollio, G. Pinto, M. DellaGreca, Allelopathy and competition between Chlorella vulgaris and Pseudokirchneriella subcapitata: Experiments and mathematical model, 2007, 208, 03043800, 205, 10.1016/j.ecolmodel.2007.05.024
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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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