关键词: 均衡点, 稳定流形定理, 最优增长路径, 土地效用指数

Abstract:

By integrating both population growths with environmental factor, utility index of land resources, and production amounts of society, and introducing a utility function with both consumption and utility index of land resources was introduced, and the optimization problem with infinite level was also presented. A three-dimension dynamic system was obtained by solving the optimization problem. It is proved that this system has unique non-zero positive equilibrium, which is a saddle.

Key words: stable manifold theorem, optimal growth path, utility index of land resources, equilibrium point