Lateral inhibition provides a unifying framework for spatiotemporal pattern formation in media comprising relaxation oscillators

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.