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Chaotic dynamics of a piecewise linear model of credit cycles

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  • Asano, Takao
  • Yokoo, Masanori

Abstract

We develop a simple piecewise linear overlapping generations model exhibiting endogenous business cycles, which is based on Matsuyama’s (2007) model of credit cycles. Some sort of “noise” representing information imperfection is shown to transform the Matsuyama model into a continuous, eventually expanding, piecewise linear map on the interval, which is tractable enough to investigate the dynamics in depth by using the techniques of the Frobenius–Perron operators to find observable chaos. While, according to the analysis of Asano et al. (2012), the Matsuyama model exhibits periodic cycles of arbitrarily large period, it is essentially not capable of chaotic dynamics. However, our model exhibits ergodic chaos with some robustness.

Suggested Citation

  • Asano, Takao & Yokoo, Masanori, 2019. "Chaotic dynamics of a piecewise linear model of credit cycles," Journal of Mathematical Economics, Elsevier, vol. 80(C), pages 9-21.
    • Handle: RePEc:eee:mateco:v:80:y:2019:i:c:p:9-21
    DOI: 10.1016/j.jmateco.2018.11.001
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    Cited by:

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    2. Hashimoto, Ken-ichi & Im, Ryonghun & Kunieda, Takuma & Shibata, Akihisa, 2022. "Financial destabilization," Journal of Mathematical Economics, Elsevier, vol. 103(C).
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    5. Takao Asano & Akihisa Shibata & Masanori Yokoo, 2021. "Polarization and Permanent Fluctuations: Quasi-Periodic Motions in a Two-Class OLG Model (Revised version with a new title "Quasi-Periodic Motions in a Polarized Overlapping Generations Model wit," KIER Working Papers 1063, Kyoto University, Institute of Economic Research.
    6. Takao Asano & Akihisa Shibata & Masanori Yokoo, 2021. "Quasi-Periodic Motions in a Polarized Overlapping Generations Model with Technology Choice," KIER Working Papers 1070, Kyoto University, Institute of Economic Research.
    7. Jos'e Pedro Gaiv~ao & Benito Pires, 2022. "Chaotic time series in financial processes consisting of savings with piecewise constant monthly contributions," Papers 2206.11933, arXiv.org, revised Feb 2023.
    8. Oscar Emilio Molina-Díaz & Gerard Olivar-Tost & Deissy Milena Sotelo-Castelblanco, 2024. "Fold-Fold Singularity in a Piecewise Smooth Mathematical Model Describing the Dynamics of a Stockless Market," Mathematics, MDPI, vol. 12(16), pages 1-18, August.

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