  The collective dynamics seen in a wide variety of chemical, biological and
ecological systems involve interactions between relaxation oscillators that
typically involve fast activation process coupled with a slower inactivation.
In this paper, we show that systems of such oscillators having distinct
kinetics governing local dynamical behavior and whose interactions are
described by different connection topologies, can exhibit strikingly similar
spatiotemporal patterns when diffusively coupled via their inactivation
component. We explain the apparent universality of this global behavior by
showing that relaxation oscillators interacting via lateral inhibition will
generally yield two basic classes of patterns, viz., one comprising one or more
clusters of synchronized oscillators while the other is a time-invariant
spatially inhomogeneous state resulting from oscillation death. All observed
collective states can be interpreted either as specific instances of these
fundamental patterns or as resulting from their competition.
