Dynamics of compositions of some Lotka–Volterra mappings operating in a two-dimensional simplex

In a number of applied problems (immunology, epidemiology, virology, etc.), there is a need to study the dynamics of the trajectories of the compositions of the Lotka–Volterra mappings. In this paper, some variants of these compositions are considered, in particular, the dynamics of the trajectories of the compositions of the Lotka–Volterra mappings acting in a two-dimensional simplex, with transitive tournaments, which can be applied in the study of these processes. Cards of fixed points are constructed for compositions and the characters of fixed points are studied.