高校招生规模、政府投入和学费标准的三维动力学模型及政府调控

近年来,随着中国高等教育招生规模的急剧扩大,高等教育中出现了许多为社会所关注的热点问题,数学建模有助于解决有关的热点问题和引导政府进行宏观调控.作者在适当的假设下,系统地建立了关于高校招生规模、政府生均经费投入与学费标准之间的3个三维非线性微分方程动力学模型.给出每个模型平衡点的稳定性条件,并通过对模型进行极值分析,得到了政府确定高校的招生基数的原则和高校招生规模的估计.其主要结果为政府进行宏观调控决策提供了相应的理论依据.

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.