On period-adding sequences of attracting cycles in piecewise linear maps

We study numerically bifurcations in a family of bimodal three-piecewise linear continuous one-dimensional maps. Attention is paid to the attracting cycles arising after the bifurcation ‘from unimodal map to bimodal map’. It is found that this type of bifurcation is accompanied by the appearance of period-adding cascades of attracting cycles γ(a11+a12k)/(a21+a22k) which are characterized by ρk = (a11 + a12k)/(a21 + a22k), k = 0, 1, …