Dynamics of Compositions of Lotka-Volterra Operators Corresponding to Some Partially Oriented Graphs in a Three-Dimensional Simplex

The paper is devoted to the study of the dynamics of the trajectories of the inner pointsof the composition of two quadratic Lotka-Volterra dynamical systems operating in a threedimensional simplex. Four compositional operators are investigated in this work. Fixed pointsare found for them and their characters are investigated by analyzing the Jacobian spectrum.Thecompositions of two discrete dynamic Lotka-Volterra systems are interesting because theycan be applied in epidemiology problems.

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