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Dynamics of a generalized fashion cycle model

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

Abstract

We study a four-parameter family of 2D piecewise linear maps with two discontinuity lines. This family is a generalization of the discrete-time version of the fashion cycle model by Matsuyama, which was originally formulated in continuous time. The parameter space of the considered map is characterised by quite a complicated bifurcation structure formed by the periodicity regions of various attracting cycles. Besides the standard period adding and period incrementing structures, there exist incrementing structures with some distinctive properties, as well as novel mixed structures, which we study in detail. The boundaries of many periodicity regions associated with border collision bifurcations of the related cycles are obtained analytically. Several mixed structures are qualitatively described.

Suggested Citation

  • Sushko, Iryna & Gardini, Laura & Matsuyama, Kiminori, 2019. "Dynamics of a generalized fashion cycle model," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 135-147.
    • Handle: RePEc:eee:chsofr:v:126:y:2019:i:c:p:135-147
    DOI: 10.1016/j.chaos.2019.06.006
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    References listed on IDEAS

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    1. Tramontana, Fabio & Sushko, Iryna & Avrutin, Viktor, 2015. "Period adding structure in a 2D discontinuous model of economic growth," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 262-273.
    2. Gian Italo Bischi & Carl Chiarella & Iryna Sushko (ed.), 2013. "Global Analysis of Dynamic Models in Economics and Finance," Springer Books, Springer, edition 127, number 978-3-642-29503-4, December.
    3. repec:hoo:wpaper:e-92-11 is not listed on IDEAS
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    Cited by:

    1. Gardini, Laura & Radi, Davide & Schmitt, Noemi & Sushko, Iryna & Westerhoff, Frank, 2023. "A 2D piecewise-linear discontinuous map arising in stock market modeling: Two overlapping period-adding bifurcation structures," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    2. Jungeilges, Jochen & Ryazanova, Tatyana, 2019. "Transitions in consumption behaviors in a peer-driven stochastic consumer network," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 144-154.
    3. Hiroshi Fujiu, 2021. "Business Cycles in a Two-Sided Altruism Model," Mathematics, MDPI, vol. 9(17), pages 1-12, August.

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