Three dimensional dynamical models for the scale of recruiting students of universities,government's devotion of outlays and standard of tuitions with applications to government's macroscopical controls

In recent years,with the rapid enlargement of the scale of recruiting students of the higher education of China,many hot problems to which the society has paid more attention have come forth.Mathematical modeling is helpful for solving the hot problems and inducting the government's behaviors of macroscopical controls.In this paper,three dynamical models of three dimensional nonlinear differential equations are systematically established for the scale of recruiting students of universities,the government's averaging devotion of outlays for students and the standard of tuitions under some assumptions.Stability conditions are given for the equilibriums of each model.A principle is given for the basic scale of recruiting students of universities which is planned by the government.The real scale of recruiting students of universities is estimated by an analysis of extrema of the models.The main results in this paper provide corresponding theoretical gists for the government to make decision-making of macroscopical controls.