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Unstable periodic orbits embedded in a chaotic economic dynamics model

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  • Ken-ichi Ishiyama
  • Yoshitaka Saiki

Abstract

We numerically find unstable periodic solutions embedded in a chaotic attractor in a generalized Goodwin model with an interaction between two countries and focus on a class of simple periodic orbits extracted from them. We confirm that chaotic behaviour represented by the model is qualitatively and quantitatively related to the unstable periodic solutions. The viewpoint in this article is based on recent work in physics. The result implies significance and usefulness of unstable periodic solutions embedded in chaotic economic dynamics.

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  • Ken-ichi Ishiyama & Yoshitaka Saiki, 2005. "Unstable periodic orbits embedded in a chaotic economic dynamics model," Applied Economics Letters, Taylor & Francis Journals, vol. 12(12), pages 749-753.
    • Handle: RePEc:taf:apeclt:v:12:y:2005:i:12:p:749-753
    DOI: 10.1080/13504850500120318
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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.
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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. El-Metwally, H., 2007. "Global behavior of an economic model," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 994-1005.
    6. 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.
    7. Stević, Stevo, 2009. "Boundedness character of a fourth order nonlinear difference equation," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2364-2369.

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