招生规模与教育质量模型的离散动力学分析

建立了招生规模与教育质量的离散动力学模型,分析了非负平衡点的存在性、稳定性与分叉,并用数值模拟验证了正平衡点的局部分叉,结果表明:政府对教育资源的投入应综合考虑教育质量对招生规模变化的敏感度以及毕业生的就业成本,最后,应用中心流形定理验证了有一个特征值为-1时正平衡点是局部稳定的.

Discrete Dynamic Analysis of Enrollment Scale and Education Quality Model

In this paper , we establish a discrete dynamic model of enrollment scale and the quality of education to analyze the existence , stability and bifurcation of the non-negative equilibrium points , and verify the local bifurcation of positive equilibrium point by numerical simulation .The results show that the government investment in education resources should take the sensitivity of the quality of education to the enrollment scale changes and the employment cost into consideration . Finally, we use Center-Manifold Theorem to verify that the positive equilibrium point is locally stability with one eigenvalue being -1.