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On a business cycle model with fractional derivative under narrow-band random excitation

Author

Listed:
  • Lin, Zifei
  • Li, Jiaorui
  • Li, Shuang

Abstract

This paper analyzes the dynamics of a business cycle model with fractional derivative of order α (0 < α < 1) subject to narrow-band random excitation, in which fractional derivative describes the memory property of the economic variables. Stochastic dynamical system concepts are integrated into the business cycle model for understanding the economic fluctuation. Firstly, the method of multiple scales is applied to derive the model to obtain the approximate analytical solution. Secondly, the effect of economic policy with fractional derivative on the amplitude of the economic fluctuation and the effect on stationary probability density are studied. The results show macroeconomic regulation and control can lower the stable amplitude of economic fluctuation. While in the process of equilibrium state, the amplitude is magnified. Also, the macroeconomic regulation and control improves the stability of the equilibrium state. Thirdly, how externally stochastic perturbation affects the dynamics of the economy system is investigated.

Suggested Citation

  • Lin, Zifei & Li, Jiaorui & Li, Shuang, 2016. "On a business cycle model with fractional derivative under narrow-band random excitation," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 61-70.
    • Handle: RePEc:eee:chsofr:v:87:y:2016:i:c:p:61-70
    DOI: 10.1016/j.chaos.2016.03.008
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    References listed on IDEAS

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    1. Sethapramote, Yuthana, 2015. "Synchronization of business cycles and economic policy linkages in ASEAN," Journal of Asian Economics, Elsevier, vol. 39(C), pages 126-136.
    2. Barseghyan, Levon & Battaglini, Marco & Coate, Stephen, 2013. "Fiscal policy over the real business cycle: A positive theory," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2223-2265.
    3. Laskin, Nick, 2000. "Fractional market dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 482-492.
    4. Dosi, Giovanni & Fagiolo, Giorgio & Roventini, Andrea, 2010. "Schumpeter meeting Keynes: A policy-friendly model of endogenous growth and business cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 34(9), pages 1748-1767, September.
    5. Gavin, William T. & Kydland, Finn E. & Pakko, Michael R., 2007. "Monetary policy, taxes, and the business cycle," Journal of Monetary Economics, Elsevier, vol. 54(6), pages 1587-1611, September.
    6. Yoshida, Hiroyuki & Asada, Toichiro, 2007. "Dynamic analysis of policy lag in a Keynes-Goodwin model: Stability, instability, cycles and chaos," Journal of Economic Behavior & Organization, Elsevier, vol. 62(3), pages 441-469, March.
    7. Chen, Wei-Ching, 2008. "Nonlinear dynamics and chaos in a fractional-order financial system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1305-1314.
    8. Matsumoto, Akio, 2009. "Note on Goodwin's 1951 nonlinear accelerator model with an investment delay," Journal of Economic Dynamics and Control, Elsevier, vol. 33(4), pages 832-842, April.
    9. Born, Benjamin & Pfeifer, Johannes, 2014. "Policy risk and the business cycle," Journal of Monetary Economics, Elsevier, vol. 68(C), pages 68-85.
    10. Li, Jiaorui & Ren, Zhengzheng & Wang, Zuoren, 2008. "Response of nonlinear random business cycle model with time delay state feedback," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(23), pages 5844-5851.
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