Dynamics of a generalized fashion cycle model

Iryna Sushko*, Laura Gardini, Kiminori Matsuyama

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)135-147
Number of pages13
JournalChaos, Solitons and Fractals
StatePublished - Sep 2019


  • 2D discontinuous piecewise linear map
  • Border collision bifurcation
  • Fashion cycle model
  • Period adding bifurcation structure
  • Period incrementing bifurcation structure

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics


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