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Journal Articles Nonlinear Studies Year : 2021

Planktons discrete-time dynamical systems

U A Rozikov
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S K Shoyimardonov
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Abstract

In this paper, we initiate the study of a discrete-time dynamical system modeling a trophic network connecting 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 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.
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Dates and versions

hal-03251221 , version 1 (12-07-2024)

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U A Rozikov, S K Shoyimardonov, R. Varro. Planktons discrete-time dynamical systems. Nonlinear Studies, 2021, 28 (2), pp.585-600. ⟨10.48550/arXiv.2001.01182⟩. ⟨hal-03251221⟩
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