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Unstable periodic orbits and chaotic economic growth

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  • Ishiyama, K.
  • Saiki, Y.

Abstract

We numerically find many unstable periodic solutions embedded in a chaotic attractor in a macroeconomic growth cycle model of two countries with different fiscal policies, and we focus on a special type of the unstable periodic solutions. It is confirmed that chaotic behavior represented by the model is qualitatively and quantitatively related to the unstable periodic solutions. We point out that the structure of a chaotic solution is dissolved into a class of finite unstable periodic solutions picked out among a large number of periodic solutions. In this context it is essential for the unstable periodic solutions to be embedded in the chaotic attractor.

Suggested Citation

  • Ishiyama, K. & Saiki, Y., 2005. "Unstable periodic orbits and chaotic economic growth," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 33-42.
    • Handle: RePEc:eee:chsofr:v:26:y:2005:i:1:p:33-42
    DOI: 10.1016/j.chaos.2004.12.012
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    References listed on IDEAS

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    1. Mario Sportelli, 1995. "A Kolmogoroff generalized predator-prey model of Goodwin's growth cycle," Journal of Economics, Springer, vol. 61(1), pages 35-64, February.
    2. A. W. Phillips, 1958. "The Relation Between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1861–1957," Economica, London School of Economics and Political Science, vol. 25(100), pages 283-299, November.
    3. Skott, Peter, 1989. "Effective Demand, Class Struggle and Cyclical Growth," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 30(1), pages 231-247, February.
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    1. Stević, Stevo, 2008. "Bounded solutions of a class of difference equations in Banach spaces producing controlled chaos," Chaos, Solitons & Fractals, Elsevier, vol. 35(2), pages 238-245.
    2. Sportelli, Mario & De Cesare, Luigi, 2022. "A Goodwin type cyclical growth model with two-time delays," Structural Change and Economic Dynamics, Elsevier, vol. 61(C), pages 95-102.
    3. Saiki, Y. & Chian, A.C.L. & Yoshida, H., 2011. "Economic intermittency in a two-country model of business cycles coupled by investment," Chaos, Solitons & Fractals, Elsevier, vol. 44(6), pages 418-428.
    4. Stević, Stevo, 2009. "Boundedness character of a fourth order nonlinear difference equation," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2364-2369.
    5. Brianzoni, Serena & Mammana, Cristiana & Michetti, Elisabetta, 2009. "Nonlinear dynamics in a business-cycle model with logistic population growth," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 717-730.
    6. Chian, Abraham C.-L. & Rempel, Erico L. & Rogers, Colin, 2006. "Complex economic dynamics: Chaotic saddle, crisis and intermittency," Chaos, Solitons & Fractals, Elsevier, vol. 29(5), pages 1194-1218.
    7. El-Metwally, H., 2007. "Global behavior of an economic model," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 994-1005.

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