Robust chaos in a credit cycle model defined by a one-dimensional piecewise smooth map

Iryna Sushko*, Laura Gardini, Kiminori Matsuyama

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


We consider a family of one-dimensional continuous piecewise smooth maps with monotone increasing and monotone decreasing branches. It is associated with a credit cycle model introduced by Matsuyama, under the assumption of the Cobb-Douglas production function. We offer a detailed analysis of the dynamics of this family. In particular, using the skew tent map as a border collision normal form we obtain the conditions of abrupt transition from an attracting fixed point to an attracting cycle or a chaotic attractor (cyclic chaotic intervals). These conditions allow us to describe the bifurcation structure of the parameter space of the map in a neighborhood of the boundary related to the border collision bifurcation of the fixed point. Particular attention is devoted to codimension-two bifurcation points. Moreover, the described bifurcation structure confirms that the chaotic attractors of the considered map are robust, that is, persistent under parameter perturbations.

Original languageEnglish (US)
Pages (from-to)299-309
Number of pages11
JournalChaos, Solitons and Fractals
StatePublished - Oct 1 2016


  • Border collision bifurcation
  • Codimension-two bifurcation
  • Homoclinic bifurcation
  • One-dimensional piecewise smooth map
  • Robust chaos
  • Skew tent map

ASJC Scopus subject areas

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


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