Pattern dynamics in a checkerboard map.
Differential equations often have solutions in the forms of trains of coherent structures such as pulses and antipulses. For such systems, the methods of singular perturbation theory permit the derivation of pattern maps that predict the sequence of spacings between successive pulses. Here we apply such a procedure to cases where two distinct kinds of pulse (or antipulse) may coexist in the system. In that case, direct application of the method leads to multivalued maps that make for complicated descriptions, especially when the succession of pulse types becomes chaotic. We show how this description may be simplified by using maps arrayed in checkerboard style to provide causal descriptions of both the successions of pulse spacings and the order in which the different kinds of pulse go by.