Waves and synchrony in networks of oscillators of relaxation and non-relaxation type

Arrays of relaxation oscillators behave differently in the presence of a non-uniformity of natural frequencies and/or coupling inputs than do arrays of phase oscillators coupled through phase differences. Phase oscillators compensate for non-uniformities by creating phase differences among the oscillators; relaxation oscillators coupled via ''fast threshold modulation'' (FTM) can respond by changing wave forms while leaving the fast jumps synchronous, For arrays of relaxation oscillators including chains, this allows synchrony to be a solution, even though the oscillators have different amounts of inputs from other oscillators; for phase-difference coupled oscillators in a chain, the generic solution is a travelling wave. Relaxation oscillators coupled through FTM also allow the encoding of patterns of oscillators into domains in which oscillators are in synchrony, with different domains in antiphase.