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

Abstract

Differential excitatory and inhibitory interactions, specifically lateral inhibition, between the constituent elements of complex systems underlie a wide range of spatiotemporal patterns in nature. Here, we show that when systems of relaxation oscillators, whose dynamics involve widely separate timescales, are coupled primarily through diffusion of the inactivation component, they exhibit strikingly similar patterns regardless of specific details of the model kinetics and spatial topology. This universality stems from the fact that all observed patterns can be viewed as either specific manifestations of, or arising through interactions between, two fundamental classes of collective dynamics, viz., a state comprising clusters of synchronized oscillators, and a time-invariant spatially inhomogeneous state resulting from oscillator death. Our work provides an unifying framework for understanding the emergent global behavior of various chemical, biological, and ecological systems spanning several time and length scales. © 2019 American Physical Society.