色噪声激励下非线性随机经济周期模型及其稳定性分析

Stability of Business Cycle Model with a Gauss Colored Noise Excitation

针对经济变量之间的非线性关系和不确定因素对经济系统的随机干扰问题,根据Goodwin消费函数和Puu函数建立了色噪声激励下的非线性动力学经济周期模型,利用统一色噪声近似原理和等效非线性化方法将模型进行了简化,由此得到了一个等效非线性白噪声模型,以获取判断动力系统稳定性的最大Lyapunov指数。研究结果表明,最大Lyapunov指数与噪声的自相关时间、边际消费率及噪声强度有关。当最大Lyapunov指数的正、负号发生变化时,系统的稳定性也随之改变。若将突发战争、国家宏观经济政策调控等经济系统的外干扰看作色噪声,边际消费作为模型参数,则在边际消费率较小的情况下可以通过加大对经济系统的干预,如国家的经济政策调整等,来稳定经济系统的发展状态。该研究结果可为实现宏观经济的持续增长研究提供参考。

For nonlinear relationships between economic variables and uncertainties to the economic system of random interference problem, a nonlinear dynamical business cycle model with Gauss colored noise is established via Goodwin consumption function and Puu investment function, and the model is simplified with a uniform colored noise approximation theory and equivalent nonlinear method. Furthermore, an equivalent nonlinear white noise model is obtained, then the largest Lyapunov exponents of the determined stability of the economic system is sought out. The approach shows that the largest Lyapunov exponent is related to the correlation time of noise, marginal consumption and noise intensity. The stability of the economic system varies with the change design of Lyapunov exponents. Choosing the sudden war, national macroeconomic policies and economic system interference as Gauss colored noise, and taking the marginal consumption as a model parameter, for the small marginal consumption rate, the economic system development can be stabilized by increasing interventions in the economic system, such as adjustment of national economic policies.