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2D discontinuous piecewise linear map: Emergence of fashion cycles

Author

Listed:
  • Laura Gardini

    (Department of Economics, Society & Politics, Università di Urbino "Carlo Bo")

  • Iryna Sushko

    (Institute of Mathematics, NASU, and Kyiv School of Economics, Ukraine)

  • Kiminori Matsuyama

    (Department of Economics, Northwestern University, USA)

Abstract

We consider a discrete-time version of the continuous-time fashion cycle model introduced in Matsuyama, 1992. Its dynamics are de?ned by a 2D discontinuous piecewise linear map depending on three parameters. In the parameter space of the map periodicity regions associated with attracting cycles of di?erent periods are organized in the period adding and period incrementing bifurcation structures. The boundaries of all the periodicity regions related to border collision bifurcations are obtained analytically in explicit form. We show the existence of several partially overlapping period incrementing structures, that is a novelty for the considered class of maps. Moreover, we show that if the time-delay in the discrete time formulation of the model shrinks to zero, the number of period incrementing structures tends to in?nity and the dynamics of the discrete time fashion cycle model converges to those of continuous-time fashion cycle model.

Suggested Citation

  • Laura Gardini & Iryna Sushko & Kiminori Matsuyama, 2017. "2D discontinuous piecewise linear map: Emergence of fashion cycles," Working Papers 1703, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2017.
    • Handle: RePEc:urb:wpaper:17_03
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    File URL: http://www.econ.uniurb.it/RePEc/urb/wpaper/WP_17_03.pdf
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    References listed on IDEAS

    as
    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. repec:hoo:wpaper:e-92-11 is not listed on IDEAS
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    2. Gardini, Laura & Sushko, Iryna & Tramontana, Fabio, 2021. "Dynamics of a two-dimensional map on nested circles and rings," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).

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