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On growing through cycles: Matsuyama’s M-map and Li–Yorke chaos

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  • Deng, Liuchun
  • Khan, M. Ali

Abstract

Recent work of Gardini et al. (2008), building on earlier work of Mitra (2001) and Mukherji (2005), considers the so-called M-map that generates a dynamical system underlying Matsuyama’s (1999) endogenous growth model. We offer proofs of the fact that there do not exist 3- or 5-period cycles in the M-map, and an example (a numerical proof) of the existence of a 7-period cycle. We use the latter, and a construction in Khan and Piazza (2011), to identify a range of parameter values of the M-map that guarantee the existence of cycles of all periods, except 3 and 5. Our argumentation relies on, and reports, the first four iterations of the M-map that may have independent interest.

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  • Deng, Liuchun & Khan, M. Ali, 2018. "On growing through cycles: Matsuyama’s M-map and Li–Yorke chaos," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 46-55.
    • Handle: RePEc:eee:mateco:v:74:y:2018:i:c:p:46-55
    DOI: 10.1016/j.jmateco.2017.10.007
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    Cited by:

    1. Ka-Kit Iong & Andreas Irmen, 2020. "The Supply of Hours Worked and Endogenous Growth Cycles," DEM Discussion Paper Series 20-10, Department of Economics at the University of Luxembourg.
    2. Aniruddha Ghosh & Mohammed Ali Khan & Metin Uyanik, 2022. "The Intermediate Value Theorem and Decision-Making in Psychology and Economics: An Expositional Consolidation," Games, MDPI, vol. 13(4), pages 1-24, July.
    3. 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.
    4. Deng, Liuchun & Khan, M. Ali, 2018. "On Mitra’s sufficient condition for topological chaos: Seventeen years later," Economics Letters, Elsevier, vol. 164(C), pages 70-74.
    5. Iong, Ka-Kit & Irmen, Andreas, 2021. "The supply of hours worked and fluctuations between growth regimes," Journal of Economic Theory, Elsevier, vol. 194(C).
    6. Hiroshi Fujiu, 2021. "Business Cycles in a Two-Sided Altruism Model," Mathematics, MDPI, vol. 9(17), pages 1-12, August.
    7. He, Sicheng, 2022. "Growing through endogenous innovation cycles," Journal of Macroeconomics, Elsevier, vol. 71(C).

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