Planktons discrete-time dynamical systems

In this paper, we initiate the study of a discrete-time dynamical system modelling a trophic network connecting the three types of plankton (phytoplankton, zooplankton, mixoplankton) and bacteria. The nonlinear operator V associated with this dynamical system is of type 4-Volterra quadratic stochast...

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Bibliographic Details
Published inarXiv.org
Main Authors Rozikov, U A, Shoyimardonov, S K, Varro, R
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 02.03.2020
Subjects
Discrete time systems
Dynamical systems
Fixed points (mathematics)
Parameters
Phytoplankton
Zooplankton
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Summary:In this paper, we initiate the study of a discrete-time dynamical system modelling a trophic network connecting the three types of plankton (phytoplankton, zooplankton, mixoplankton) and bacteria. The nonlinear operator V associated with this dynamical system is of type 4-Volterra quadratic stochastic operator (QSO) with twelve parameters. We give conditions on the parameters under which this operator maps the five-dimensional standard simplex to itself and we find its fixed points. Moreover, we study the limit points of trajectories for this operator. For each situations we give some biological interpretations.
ISSN:2331-8422