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Discrete Dynamics in Nature and Society
Volume 2013, Article ID 275134, 9 pages
Research Article

Modeling of Macroeconomics by a Novel Discrete Nonlinear Fractional Dynamical System

Business School, Central South University, Changsha, Hunan 410083, China

Received 2 July 2013; Accepted 12 November 2013

Academic Editor: Zhen Jin

Copyright © 2013 Zhenhua Hu and Wen Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We propose a new nonlinear economic system with fractional derivative. According to the Jumarie’s definition of fractional derivative, we obtain a discrete fractional nonlinear economic system. Three variables, the gross domestic production, inflation, and unemployment rate, are considered by this nonlinear system. Based on the concrete macroeconomic data of USA, the coefficients of this nonlinear system are estimated by the method of least squares. The application of discrete fractional economic model with linear and nonlinear structure is shown to illustrate the efficiency of modeling the macroeconomic data with discrete fractional dynamical system. The empirical study suggests that the nonlinear discrete fractional dynamical system can describe the actual economic data accurately and predict the future behavior more reasonably than the linear dynamic system. The method proposed in this paper can be applied to investigate other macroeconomic variables of more states.