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 d o arrays of phase oscillators coupled through phase differences. Phase oscillators compensate for non-uniformities by creating phase differe nces 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 oscillato rs including chains, this allows synchrony to be a solution, even thou gh the oscillators have different amounts of inputs from other oscilla tors; 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 i n which oscillators are in synchrony, with different domains in antiph ase.