К ВОПРОСУ ПРОГНОЗИРОВАНИЯ ПРОДВИЖЕНИЯ УНИВЕРСИТЕТОВ В ГЛОБАЛЬНЫХ УНИВЕРСИТЕТСКИХ РЕЙТИНГАХ

Abstract

A simplified approach to solving the equations of population dynamics (Lotka–Volterra equations), which is a nonlinear multidimensional system of ordinary differential equations of the first order, describing the competitive interaction of universities included in some world university ranking, is proposed. The phase variables in these equations are the values of the integral indicator of the university ranking, which is called Overall or Total Score. The simplification consists in reducing this system to a system of independent Verhulst equations with analytic solutions in exponents of time and passing from them to stationary solutions when time tends to infinity. It is shown that with this approach and a given growth rate Overall (Total) Score, it is possible to find symmetric coefficients of interuniversity competition for no more than three competing universities. When finding such coefficients for the first three universities in the THE ranking, numerical solutions of the original system of population dynamics equations were obtained using the Runge–Kutta method in MatLab. It is shown that the development of this approach, based on the equations of population dynamics, can consist in turning to the concept of competitive – cooperative university interactions. The system of differential equations describes the process of changing the integral indicator during the period between two ratings. Using the found values of the coefficients of interuniversity competition, the system is solved sequentially for all stages of the ranking, and the decisions at the previous stage are used as the initial conditions for the next one.