带有环境净化的双随机参数SOLOW模型的稳定性  

The Stability of the SOLOW Model with Double Random Parameters based on Environmental Purification

作　　者：李佼瑞[1] 张艳霞[1] 

机构地区：[1]西安财经学院统计学院,陕西西安710100

出　　处：《统计与信息论坛》2016年第6期7-13,共7页Journal of Statistics and Information

基　　金：国家自然科学基金项目<经济-环境系统的分数阶随机动力学建模与分析>(11572231)

摘　　要：考虑到环境净化能力和劳动力的相对变化率均含有大量不确定性因素,研究带有环境净化和两个随机参数的Solow模型的稳定性问题。在对带有环境净化的Solow模型的研究中引入两个独立的随机参数:基于环境净化能力和劳动力的相对变化率,建立带有双随机参数的Solow模型;利用Chebyshev正交多项式逼近原理,将随机模型转化为等价的确定性近似系统,由Routh-Hurwitz判据理论和数值方法,研究随机系统定态渐近稳定性的条件,结果表明:带有双随机参数和环境净化Solow模型的稳定性受随机参数强度的影响较大,随着随机强度的增大,渐进稳定性区域不断减小,即经济增长与环境净化系统的协调发展区域缩小。Considering the both environmental purification capacity and relative rate of change of the labor force contain lots of uncertainty factors,so in the studying of the SOLOW model with environmental purification,two independent random parameters which express environmental purification capacity and relative rate of change of the labor force respectively are introduced,then the SOLOW model with double stochastic parameters is established.The stochastic model can be converted to equivalent deterministic approximate system using the Chebyshev orthogonal polynomial approximation principle.By applying the Routh Hurwitz criterion theory and numerical method,the asymptotic stability conditions of stationary state of the random system are obtained.The result shows that the stability of the Solow model with double random parameters and environmental purification is greatly influenced by the strength of random parameters,and with the increasing of the random strengths,the asymptotic stability area will decrease continuously which means the coordinated development area of economic growth and environment purification system will shrink.

关 键 词：SOLOW模型 双随机参数 正交展开逼近 渐近稳定性 

分 类 号：F224.0[经济管理—国民经济]