Asymmetry and General Integral of a Dynamic System and Its Application in Higher Education

In this study, we applied dynamical system theory to analyze evolutionary trends of the higher education system, consisting of three indicators: university scale development, government financial investment, and student fee standards. The higher education system has significant uncertainty over a long period of evolution, especially with the development scale and speed of higher education largely depending on government financial investment and changes in student fee standards. We adopted the theory and methods of dynamical system theory to analyze the evolutionary trend of the higher education system, composed of these three indicators. Using the principles and methods of differential dynamics, we put forward a three-dimensional dynamic system model, involving variables such as higher education scale expansion, standard of tuition, and government financial investment. Based on the qualitative theory of ordinary differential equations, we have obtained the stability conditions for the equilibrium of the dynamic model and the conclusion of the asymptotic of the asymmetric solution of the three-dimensional dynamical system. The general integral expression of the system was obtained under specific conditions. The general integral can explain the global structure of the system in some aspects, and can compensate for the shortcomings of the local structure of equilibrium points.