基于分数阶导数的经济波动模型的稳定性研究

STABILITYANALYSIS OF ANECONOMIC FLUCTUATION MODEL WITH FRACTIONAL DERIVATIVE

分析了含有分数阶导数的经济波动模型,其中分数阶导数描述了经济变量的长记忆性质.将随机动力系统的概念引入到了经济波动模型以理解经济波动的本质特征.主要研究了经济波动问题中的平衡状态的稳定性以及经济波动的波动幅度问题.首先,我们研究了经济变量的记忆性质对经济波动的稳定性和波动幅度的影响.结果表明,经济变量的长记忆性延长了经济系统到达平衡状态的时间,这对宏观经济调控提供了一个新的视角和观点.其次,我们研究了分数阶导数如何影响和改变经济波动的波动幅度.结果显示相比于经典模型,经济变量的时间记忆特性会产生不同的令人惊奇的现象.

This paper analyzes the dynamics of economic fluctuation model with fractional derivative of order α （0〈α〈1）, in which fractional derivative depicts the viscoelasticity of the economy system （the so-called memory and hereditary properties of economic variables）. Dynamical system concepts are integrated into the business cycle model for understanding the economic fluctuation. Stability and amplitude of an economy system with fractional derivative are studied and comparedwith classical Goodwin model. Firstly, the influence of the memory property of economic variables on the stability of the economy system is investigated. The result show that an economy system with fractional derivative cost more time to be the equilibrium state. It proposes a new view on the macroeeonomic regulation and control policy. Secondly, how fractional derivatives influence and transform the amplitude of the economic fluctuation is studied, and the results show that memory property of economic variables can lead to some different phenomena comparing with the model without considering the memory property of economic variables.