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Superstable credit cycles and U-sequence

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  • Sushko, Iryna
  • Gardini, Laura
  • Matsuyama, Kiminori

Abstract

We study a particular bifurcation structure observed in the parameter space of a one-dimensional continuous piecewise smooth map generated by the credit cycle model introduced by Matsuyama, where the map is defined over the absorbing interval via three functions, one of which is a constant. We show that the flat branch gives rise to superstable cycles whose periodicity regions are ordered according to a modified U-sequence and accumulate to the curves related to homoclinic cycles which represent attractors in Milnor sense. The boundaries of these regions correspond to fold and flip border collision bifurcations of the related superstable cycles.

Suggested Citation

  • Sushko, Iryna & Gardini, Laura & Matsuyama, Kiminori, 2014. "Superstable credit cycles and U-sequence," Chaos, Solitons & Fractals, Elsevier, vol. 59(C), pages 13-27.
    • Handle: RePEc:eee:chsofr:v:59:y:2014:i:c:p:13-27
    DOI: 10.1016/j.chaos.2013.11.006
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    1. Cars Hommes & Helena Nusse, 1991. "“Period three to period two” bifurcation for piecewise linear models," Journal of Economics, Springer, vol. 54(2), pages 157-169, June.
    2. Sushko, Iryna & Agliari, Anna & Gardini, Laura, 2006. "Bifurcation structure of parameter plane for a family of unimodal piecewise smooth maps: Border-collision bifurcation curves," Chaos, Solitons & Fractals, Elsevier, vol. 29(3), pages 756-770.
    3. Futter, Ben & Avrutin, Viktor & Schanz, Michael, 2012. "The discontinuous flat top tent map and the nested period incrementing bifurcation structure," Chaos, Solitons & Fractals, Elsevier, vol. 45(4), pages 465-482.
    4. Fabio Tramontana & Laura Gardini & Frank Westerhoff, 2011. "Heterogeneous Speculators and Asset Price Dynamics: Further Results from a One-Dimensional Discontinuous Piecewise-Linear Map," Computational Economics, Springer;Society for Computational Economics, vol. 38(3), pages 329-347, October.
    5. Kiminori Matsuyama, 2007. "Credit Traps and Credit Cycles," American Economic Review, American Economic Association, vol. 97(1), pages 503-516, March.
    6. ,, 2013. "The good, the bad, and the ugly: An inquiry into the causes and nature of credit cycles," Theoretical Economics, Econometric Society, vol. 8(3), September.
    7. Brianzoni, Serena & Michetti, Elisabetta & Sushko, Iryna, 2010. "Border collision bifurcations of superstable cycles in a one-dimensional piecewise smooth map," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(1), pages 52-61.
    8. Kiminori Matsuyama, 2001. "Good and Bad Investment: An Inquiry into the Causes of Credit Cycles," Discussion Papers 1335, Northwestern University, Center for Mathematical Studies in Economics and Management Science, revised Sep 2001.
    9. Gardini, Laura & Sushko, Iryna & Naimzada, Ahmad K., 2008. "Growing through chaotic intervals," Journal of Economic Theory, Elsevier, vol. 143(1), pages 541-557, November.
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    Cited by:

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    2. Kubin, Ingrid & Zörner, Thomas O. & Gardini, Laura & Commendatore, Pasquale, 2019. "A credit cycle model with market sentiments," Structural Change and Economic Dynamics, Elsevier, vol. 50(C), pages 159-174.
    3. Sushko, Iryna & Gardini, Laura & Matsuyama, Kiminori, 2016. "Robust chaos in a credit cycle model defined by a one-dimensional piecewise smooth map," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 299-309.
    4. Laura Gardini & Roya Makrooni & Iryna Sushko, 2016. "Cascades of Alternating Smooth Bifurcations and Border Collision Bifurcations in a Family of Discontinuous Linear-Power Maps," Gecomplexity Discussion Paper Series 201603, Action IS1104 "The EU in the new complex geography of economic systems: models, tools and policy evaluation", revised Mar 2016.
    5. Takao Asano & Akihisa Shibata & Masanori Yokoo, 2024. "Technology choice, externalities in production, and a chaotic middle-income trap," Journal of Economics, Springer, vol. 141(1), pages 29-56, January.
    6. Matsuyama, Kiminori & Sushko, Iryna & Gardini, Laura, 2016. "Revisiting the model of credit cycles with Good and Bad projects," Journal of Economic Theory, Elsevier, vol. 163(C), pages 525-556.
    7. Radi, Davide & Gardini, Laura, 2015. "Entry limitations and heterogeneous tolerances in a Schelling-like segregation model," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 130-144.
    8. Ingrid Kubin & Laura Gardini, 2022. "On the significance of borders: the emergence of endogenous dynamics," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 17(1), pages 41-62, January.
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    10. Roya Makrooni & Laura Gardini, 2015. "Bifurcation structures in a family of one-dimensional linear-power discontinuous maps," Gecomplexity Discussion Paper Series 7, Action IS1104 "The EU in the new complex geography of economic systems: models, tools and policy evaluation", revised Jan 2015.

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