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 inNonlinear studies Vol. 28; no. 2; pp. 585 - 600
Main Authors Rozikov, U. A, Shoyimardonov, S. K, Varro, R
Format Journal Article
LanguageEnglish
Published Cambridge Scientific Publishers 22.05.2021
Subjects
Commutative Algebra
Mathematics
Mathematics - Dynamical Systems
Dynamical Systems (math.DS)
37N25
FOS: Mathematics
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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:1359-8678
2153-4373
DOI:10.48550/arxiv.2001.01182