Activation process in excitable systems with multiple noise sources: Large number of units

TL;DR

This paper investigates how large assemblies of excitable units with multiple noise sources can exhibit macroscopic excitable behavior, revealing insights into collective activation dynamics and stochastic bifurcations.

Contribution

The study introduces three formulations of assembly activation events and demonstrates that collective behavior mirrors single-unit dynamics through stochastic bifurcations.

Findings

Assembly exhibits macroscopic excitable behavior similar to single units.

Global variables undergo stochastic bifurcation from stable fixed point to oscillations.

System-size anti-resonance affects mean activation time.

Abstract

We study the activation process in large assemblies of type II excitable units whose dynamics is influenced by two independent noise terms. The mean-field approach is applied to explicitly demonstrate that the assembly of excitable units can itself exhibit macroscopic excitable behavior. In order to facilitate the comparison between the excitable dynamics of a single unit and an assembly, we introduce three distinct formulations of the assembly activation event. Each formulation treats different aspects of the relevant phenomena, including the threshold-like behavior and the role of coherence of individual spikes. Statistical properties of the assembly activation process, such as the mean time-to-first pulse and the associated coefficient of variation, are found to be qualitatively analogous for all three formulations, as well as to resemble the results for a single unit. These analogies are shown to derive from the fact that global variables undergo a stochastic bifurcation from the stochastically stable fixed point to continuous oscillations. Local activation processes are analyzed in the light of the competition between the noise-led and the relaxation-driven dynamics. We also briefly report on a system-size anti-resonant effect displayed by the mean time-to-first pulse.