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A stochastic modelling of phytoplankton aggregation

Abstract : The aim of this work is to provide a stochastic mathematical model of aggregation in phytoplankton, from the point of view of modelling a system of a large but finite number of phytoplankton cells that are subject to random dispersal, mutual interactions allowing the cell motions some dependence and branching (cell division or death). We present the passage from the ''microscopic'' description to the ''macroscopic'' one, when the initial number of cells tends to infinity (large phytoplankton populations). The limit of the system is an extension of the Dawson-Watanabe superprocess: it is a superprocess with spatial interactions which can be described by a nonlinear stochastic partial differential equation.
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Nadjia El Saadi, Ovide Arino. A stochastic modelling of phytoplankton aggregation. Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées, INRIA, 2006, 5, pp.80-94. ⟨hal-01263454⟩

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