Methods of mathematical modeling for predicting university entry into TOP-100 world university rankings

Abstract

Subject. The article focuses on mathematical methods for predicting university entry into TOP-100 World University Rankings. Objectives. The purpose of the study is to develop mathematical modeling techniques for predicting university entry into TOP-100 World University Rankings. Methods. We consider two approaches in mathematical simulation for the said purpose. The first approach employs population dynamics equations, including the Verhulst and the Lotka-Volterra equations. The second approach uses linear algebraic equation in three variables together with the variables constraints. Results. Population dynamics equations enable to model improvement in university performance expressed by Total Score or Overall Score indicator, to define intra-university competition and competition between universities of the World University Rankings. Linear algebraic equations provide projections of a university's specified position in the world rankings. We made clear mathematical statement of the problems; solved the problem that relates to entering TOP-100 of three global rankings (ARWU, THE, QS) by the Moscow State University and St. Petersburg University. Conclusions. We assume that the offered approaches will be useful for university managers who monitor and guide their university positioning.