%0 Journal Article
%T Modeling of Macroeconomics by a Novel Discrete Nonlinear Fractional Dynamical System
%A Zhenhua Hu
%A Wen Chen
%J Discrete Dynamics in Nature and Society
%D 2013
%I Hindawi Publishing Corporation
%R 10.1155/2013/275134
%X 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. 1. Introduction Economic dynamics has recently become more prominent in mainstream economics. This influence has been quite pervasive and has influenced both microeconomics and macroeconomics. Its influence in macroeconomics, however, has been much greater. In the real-world life, economic evolution behaves like some process with inner random property. The investigation of economic system gains much development in the recent decades mainly since it can exhibit ubiquitous complex dynamics evidenced by large-amplitude and aperiodic fluctuations [1¨C3]. For instance, the study of economic system by using van del Pol equation is discussed in [4]. The variation of initial conditions and control parameters of the van del Pol model enables us to understand the periodic, quasiperiodic, and chaotic motion of economic variable considered. In [5, 6], the bifurcation topological structure and the global complicated character of a kind of nonlinear financial system are studied. A simplified macroeconomic model discussing the investment, interest rate, and price index is proposed and various evolution results of these economic variables depending on time and parameters are illustrated. Generally speaking, among these prices of literature we may find many mathematical conclusions of economic system, which are helpful to study the dynamical properties of economic models in depth. However, in the above literature, only integer order differential equations are investigated. In the recent years, it is found that depicting the real-world problem by using model with fractional derivative will provide more
%U http://www.hindawi.com/journals/ddns/2013/275134/