Superstable credit cycles and U-sequence

Highlights: • A family of one-dimensional piecewise smooth maps is considered, defined by an increasing, decreasing and flat branches. • The map describes macroeconomic dynamics of credit cycles. • Nonsmoothness and a flat branch give rise to periodicity regions ordered according to a modified U-sequence. • The boundaries of the periodicity regions are related to fold and flip border collision bifurcations. • Milnor attractors are described, associated with homoclinic bifurcations. -- 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