综合国力非线性扩散模型稳定性分析

Stability analysis of nonlinear diffusion model describing comprehensive national power

研究了一般综合国力非线性扩散数学模型及其相应简化的综合国力非线性扩散数学模型的全局渐近稳定性与部分变元全局稳定,其余部分变元稳定的构造性判据.具体方法是仅根据模型的系数,构造出在Rn+内正定径向无界的Lyapunov函数,再估算Lyapunov函数沿模型的导数符号判别模型的解在Rn+内关于平衡位置的全局稳定性与部分全局稳定性,并说明了各种综合指标的相互影响、相互制约以及比例协调对动态平衡的作用.

In this paper, the general nonlinear diffusion model of comprehensive national power and its corresponding simplified model are studied. And the latter model＇s constructive criteria for the asymptotic global stability of all arguments, the asymptotic global stability of some partial arguments as well as the stability of others are also researched. Concretely speaking, the Lyapunov Function with positive definite unbounded radial flow in R^n＋ is constructed based on the coefficients of the model. Then the asymptotic global stability of all arguments and that of some partial arguments of the solutions, obtained from Lyapunov Function along the model of derivative sign criteria, in the model＇s equilibrium position within R^n＋ are evaluated. The results show the effect of the interaction, mutual restriction and harmonious proportion among all comprehensive indexes on dynamic equilibrium.