Discrete Dynamical Systems of Lotka–Volterra and Their Applications on the Modeling of the Biogen Cycle in Ecosystem

Investigation of many problems of population genetics, epidemiology, ecology, etc. leads to the study of quadratic simplex mappings, a prominent representative of which are the Lotka–Volterra mappings. In this paper, we consider Lotka–Volterra mappings acting in a four-dimensional simplex with homogeneous tournaments. These mappings are interesting in that they can be offered as a model for studying the elements of living matter coming from the environment, which, having passed through a number of organisms, return to the external environment, and then are again included in the composition of living matter. For a more detailed study of the considered mappings, cards of fixed points are constructed and studied. According to the structure of the card, it is possible to represent the cycles of carbon and phosphorus.

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