Bandcount adding structure and collapse of chaotic attractors in a piecewise linear bimodal map

In this work we investigate bifurcation structures in the chaotic domain of a piecewise linear bimodal map. The map represents a model of a circuit proposed to generate chaotic signals. For practical purposes it is necessary that the map generates robust broad-band chaos. However, experiments show that this requirement is fulfilled not everywhere. We show that the chaotic domain in the parameter space of this map contains regions in which the map has multi-band chaotic attractors. These regions are confined by bifurcation curves associated with homoclinic bifurcations of unstable cycles, and form a so-called bandcount adding structure previously reported to occur in discontinuous maps. Additionally, it is shown that inside each of these regions chaotic attractors collapse to particular cycles existing on a domain of zero measure in the parameter space and organized in a period adding structure in the form known for circle maps.