Stabilityanalysis of aneconomic fluctuation model with fractional derivative

This paper analyzes the dynamics of economic fluctuation model with fractional derivative of order a (0 <ot < 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 lime to be the equilibrium state. It proposes a new view on the macroeconomic 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.