Bigraphs and Dynamics of Lotka–Volterra Mapping Trajectories on a Four-Dimensional Simplex Δ⁴

In this paper, the dynamic properties of the Lotka–Volterra mapping are investigated, the matrix of which is determined by a complete oriented bigraph. Previously, such Lotka–Volterra mappings were not considered. In the framework of these mappings, criteria for trajectory convergence and the associated pathways of positive and negative trajectories are determined. It is shown that, in some degenerate cases, it is possible not only to establish conditions for the convergence of trajectories but also to determine the beginning and end of the evolution of any trajectory. The discrete mappings studied in this paper can act as a discrete compartmental model divided into three groups and including viruses that replicate only in the presence of other viruses.