Bandcount incrementing scenario revisited and floating regions within robust chaos

When dealing with piecewise-smooth systems, the chaotic domain often does not contain any periodic inclusions, which is called “robust chaos”. Recently, the bifurcation structures in the robust chaotic domain of 1D piecewise-linear maps were investigated. It was shown that several regions of multi-band chaotic attractors emerge at the boundary between the periodic and the chaotic domain, forming complex self-similar bifurcation structures. However, some multi-band regions were observed also far away from this boundary. In this work we consider the question how these regions emerge and how they become disconnected from the boundary.