Behavior Dynamics of the Lotka-Volterra Mapping Composition, with Transitive tournaments describing models of sexually transmitted diseases

Abstract

Mathematical ecology as a science began to take shape at the beginning of the XX century Its emergence was facilitated by the works of outstanding mathematicians like Vito Volterra and his contemporaries L Lotka and V A Kostitsin Further development of mathematical ecology is associated with the names of G F Gause A N Kolmogorov Yu Odum Yu M Svirezhev R A Poluektov etc Mathematical methods have penetrated most deeply into the study of the dynamics of the number of biological populations which occupy a central place in the problems of ecology and population genetics The paper considers the composition of two Lotka-Volterra mappings operating in a two-dimensional simplex with transitive tournaments with two inversely directed edges since the composition can be used to simulate sexually transmitted diseases All fixed points are found for the composition and their characters are studied as well as the dynamics of the asymptotic behavior of the trajectory i e the phase portrait is shown for each component of the composition