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Open AccessArticle

Study on the Business Cycle Model with Fractional-Order Time Delay under Random Excitation

1
Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, China
2
School of Statistics, Xi’an University of Finance & Economics, Xi’an 710061, China
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Author to whom correspondence should be addressed.
Entropy 2017, 19(7), 354; https://doi.org/10.3390/e19070354
Received: 31 May 2017 / Revised: 2 July 2017 / Accepted: 10 July 2017 / Published: 12 July 2017
(This article belongs to the Special Issue Complex Systems, Non-Equilibrium Dynamics and Self-Organisation)
Time delay of economic policy and memory property in a real economy system is omnipresent and inevitable. In this paper, a business cycle model with fractional-order time delay which describes the delay and memory property of economic control is investigated. Stochastic averaging method is applied to obtain the approximate analytical solution. Numerical simulations are done to verify the method. The effects of the fractional order, time delay, economic control and random excitation on the amplitude of the economy system are investigated. The results show that time delay, fractional order and intensity of random excitation can all magnify the amplitude and increase the volatility of the economy system. View Full-Text
Keywords: business cycle model; fractional derivative; random excitation; time delay; stochastic averaging method business cycle model; fractional derivative; random excitation; time delay; stochastic averaging method
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Lin, Z.; Xu, W.; Li, J.; Jia, W.; Li, S. Study on the Business Cycle Model with Fractional-Order Time Delay under Random Excitation. Entropy 2017, 19, 354.

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