Abstract
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 language | English (US) |
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Pages (from-to) | 13-27 |
Number of pages | 15 |
Journal | Chaos, Solitons and Fractals |
Volume | 59 |
DOIs | |
State | Published - Feb 2014 |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- General Mathematics
- General Physics and Astronomy
- Applied Mathematics