Macroscopic behavior of populations of quadratic integrate-and-fire neurons subject to non-Gaussian white noise

Denis S Goldobin; Evelina V Permyakova; Lyudmila S Klimenko

doi:10.1063/5.0172735

Macroscopic behavior of populations of quadratic integrate-and-fire neurons subject to non-Gaussian white noise

Chaos. 2024 Jan 1;34(1):013121. doi: 10.1063/5.0172735.

Authors

Denis S Goldobin^{1

2}, Evelina V Permyakova¹, Lyudmila S Klimenko^{1

3}

Affiliations

¹ Institute of Continuous Media Mechanics, UB RAS, Academician Korolev Street 1, 614013 Perm, Russia.
² Department of Control Theory, Nizhny Novgorod State University, Gagarin Avenue 23, 603022 Nizhny Novgorod, Russia.
³ Department of Theoretical Physics, Perm State University, Bukirev Street 15, 614990 Perm, Russia.

PMID: 38242105
DOI: 10.1063/5.0172735

Abstract

We study macroscopic behavior of populations of quadratic integrate-and-fire neurons subject to non-Gaussian noises; we argue that these noises must be α-stable whenever they are delta-correlated (white). For the case of additive-in-voltage noise, we derive the governing equation of the dynamics of the characteristic function of the membrane voltage distribution and construct a linear-in-noise perturbation theory. Specifically for the recurrent network with global synaptic coupling, we theoretically calculate the observables: population-mean membrane voltage and firing rate. The theoretical results are underpinned by the results of numerical simulation for homogeneous and heterogeneous populations. The possibility of the generalization of the pseudocumulant approach to the case of a fractional α is examined for both irrational and fractional rational α. This examination seemingly suggests the pseudocumulant approach or its modifications to be employable only for the integer values of α=1 (Cauchy noise) and 2 (Gaussian noise) within the physically meaningful range (0;2]. Remarkably, the analysis for fractional α indirectly revealed that, for the Gaussian noise, the minimal asymptotically rigorous model reduction must involve three pseudocumulants and the two-pseudocumulant model reduction is an artificial approximation. This explains a surprising gain of accuracy for the three-pseudocumulant models as compared to the two-pseudocumulant ones reported in the literature.