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arXiv · 1507.03254

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

Igor Franović·Matjaz Perc·Kristina Todorović·Srđan Kostić·Nikola Burić
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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.

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Igor Franović, Matjaz Perc, Kristina Todorović, Srđan Kostić, Nikola Burić. 2015-11-24. Activation process in excitable systems with multiple noise sources: Large number of units. https://doi.org/10.1103/physreve.92.062912

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