We continue the investigation of a one-dimensional piecewise linear map with two discontinuity points. Such a map may arise from a simple asset-pricing model with heterogeneous speculators, which can help us to explain the intricate bull and bear behavior of financial markets. Our focus is on bifurcation structures observed in the chaotic domain of the map's parameter space, which is associated with robust multiband chaotic attractors. Such structures, related to the map with two discontinuities, have been not studied before. We show that besides the standard bandcount adding and bandcount incrementing bifurcation structures, associated with two partitions, there exist peculiar bandcount adding and bandcount incrementing structures involving all three partitions. Moreover, the map's three partitions may generate intriguing bistability phenomena.
Recall that a basic cycle has only one point in the left (right) partition of the map, while all its other points are located in the right (left) partition.
Clearly, if one point of cycle collides with a particular image of a critical point, the other points of also collide with respective images of the same critical point. We choose the point of that collides with image of the smallest rank, to get the simplest expression for the bifurcation condition.