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

Abstract

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.

The interplay of inhibitory and electrical synapses results in complex persistent activity

“…We report here, the existence of chimera pattern that comprises neurons exhibiting both oscillatory and non-oscillatory states. Such chimera patterns have been reported in our earlier study [61] in the context of biological pattern formation. Studies on networks of excitatory and/or inhibitory with synapse and gapjunctions have shown to give complex spatiotemporal dynamics, viz.…”

Disorder in cellular packing can alter proliferation dynamics to regulate growth

“…Our work also suggests a causal relation between the simultaneous increase in regularity of the L052401-4 planar arrangement of cells in growing epithelial tissue and the arrest of growth in the cellular assembly in normal development (i.e., strong coupling) [40,50,51]. It further suggests that heterogeneous contact topology in networks of oscillators interacting via lateral inhibition [52] will increase the range over which chimera states, characterized by the coexistence of oscillating and nonoscillating elements [53], are likely to occur.…”

Disorder in cellular packing can alter proliferation dynamics to regulate growth

“…Thus, our results suggest a causal relation between the observation of the simultaneous increase in regularity in the planar arrangement of cells in growing epithelial tissue and the arrest of growth in the cellular assembly, that occur together over the normal course of development [34,44,45]. Indeed, it hints that, in general, heterogeneous contact topology in networks of oscillators interacting via lateral inhibition [46] will increase the range of interaction strengths over which chimera states, characterized by coexistence of oscillating and non-oscillating elements [47], are likely to appear.…”