Properties and features of asymmetric partial devil’s staircases deduced from piecewise linear maps

A piecewise linear map with one discontinuity is used to link together iterated map properties with the shape of the ensuing staircases. In the main part of the paper, a three-segment map is treated, with a horizontal middle segment next to the discontinuity and the development of partial and asymmetric staircases is demonstrated. In particular, a possible hierarchy of partiality, connected with the ratio of the length of the horizontal segment to the discontinuity jump, is obtained. The map is used for constructing staircases that imitate various experimental and numerical staircases that appear in the literature for excitable systems.