Superstable credit cycles and U-sequence

Iryna Sushko*, Laura Gardini, Kiminori Matsuyama

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


We study a particular bifurcation structure observed in the parameter space of a one-dimensional continuous piecewise smooth map generated by the credit cycle model introduced by Matsuyama, where the map is defined over the absorbing interval via three functions, one of which is a constant. We show that the flat branch gives rise to superstable cycles whose periodicity regions are ordered according to a modified U-sequence and accumulate to the curves related to homoclinic cycles which represent attractors in Milnor sense. The boundaries of these regions correspond to fold and flip border collision bifurcations of the related superstable cycles.

Original languageEnglish (US)
Pages (from-to)13-27
Number of pages15
JournalChaos, Solitons and Fractals
StatePublished - Feb 2014

ASJC Scopus subject areas

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


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