Basins of fixed points for composition of the Lotka-Volterra mappings and their classification (Q6040390)

The authors study the composition of two Lotka-Volterra mappings which are mutually inverse transitive tournaments. When the domain of definition is restricted to a hyperplane, there exist two real lines which are invariant under the action of the composite mapping. Therefore, the analysis can be performed using the theory of one-dimensional discrete dynamics. By using a graphical analysis method, the basins of fixed points on these two real lines are found. The composition of two Lotka-Volterra mappings can be applied to epidemiological models. The investigation is useful in understanding the dynamics of viral diseases transmitted by direct contact in patients who have concomitant diseases.