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Entropy 2016, 18(9), 332; doi:10.3390/e18090332

Study on the Inherent Complex Features and Chaos Control of IS–LM Fractional-Order Systems

Nonlinear Dynamics and Chaos Group, College of Management and Economics, Tianjin University, Tianjin 300072, China
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Academic Editors: Carlo Cattani and Kevin H. Knuth
Received: 24 June 2016 / Revised: 24 August 2016 / Accepted: 5 September 2016 / Published: 14 September 2016
(This article belongs to the Special Issue Wavelets, Fractals and Information Theory II)
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Abstract

Based on the traditional IS–LM economic theory, which shows the relationship between interest rates and output in the goods and services market and the money market in macroeconomic. We established a four-dimensional IS–LM model involving four variables. With the Caputo fractional calculus theory, we improved it into a fractional order nonlinear model, analyzed the complexity and stability of the fractional order system. The existences conditions of attractors under different order conditions are compared, and obtain the orders when the system reaches a stable state. Have the detail analysis on the dynamic phenomena, such as the strange attractor, sensitivity to initial values through phase diagram and the power spectral. The order changes in two ways: orders changes synchronously or single order changes. The results show regardless of which the order situation is, the economic system will enter into multiple states, such as strong divergence, strange attractor and the convergence, finally, system will enter into the stable state under a certain order; parameter changes have similar effects on the economic system. Therefore, selecting an appropriate order is significant for an economic system, which guarantees a steady development. Furthermore, this paper construct the chaos control to IS–LM fractional-order macroeconomic model by means of linear feedback control method, by calculating and adjusting the feedback coefficient, we make the system return to the convergence state. View Full-Text
Keywords: fractional order; IS–LM system; complexity; dynamic characteristics evolution; chaos control fractional order; IS–LM system; complexity; dynamic characteristics evolution; chaos control
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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. (CC BY 4.0).

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Ma, J.; Ren, W.; Zhan, X. Study on the Inherent Complex Features and Chaos Control of IS–LM Fractional-Order Systems. Entropy 2016, 18, 332.

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