We demonstrate that complex sequences of periodic states such as those observed in the Belousov Zhabotinsky reaction can be generated by simple one-dimensional maps. Motivated by the experimental data, we construct a map which reproduces most of the complicated devil's staircase observed by Maselko and Swinney as well as chaos and other experimentally observed periodic sequences. An interesting property of the devil's staircase observed here is that it remains complete through a wide range of parameters, in contrast to the devil's staircases observed in critical circle maps. We also comment on a new class of mode-locking sequences.
Bagley, R.J., Farmer, J.D. & Mayer-Kress, G. (1986). 'Mode Locking, The Belousov-Zhabotinsky Reaction, and One-Dimensional Mappings'. Physics Letters, 114A(8), pp.419-423.