Noise-driven amplification mechanisms governing the emergence of coherent extreme events in excitable systems

The physics governing the formation of extreme coherent events, i.e., the systemwide emergence of an observable taking extraordinary values in a short time window, is a relevant yet elusive problem to a variety of disciplines ranging from climate science to neuroscience. Despite their inherent differences, systems exhibiting episodes of extreme coherence can be abstracted as a set of coupled nonlinear elements in a noisy and networked environment. Here, we propose a model describing the generation of extreme coherence by exploring theoretically and numerically the capacity of noise and network correlations to amplify a critical core of the system and trigger an extreme event. Although we principally center our study in modeling bursting phenomena in neuronal circuits, we extend our analysis to other systems such as algae blooms and infectious diseases. We show that extreme events originate in a relatively small core of the system and that different cores may coexist. We also show that the amplification mechanisms within a system are highly robust, so that the deletion of central nodes leads to other nodes taking leadership.