A reduction methodology for fluctuation driven population dynamics

Abstract

Lorentzian distributions have been largely employed in statistical mechanics to obtain exact results for heterogeneous systems. Analytic continuation of these results is impossible even for slightly deformed Lorentzian distributions, due to the divergence of all the moments (cumulants). We have solved this problem by introducing a `pseudo-cumulants' expansion. This allows us to develop a reduction methodology for heterogeneous spiking neural networks subject to extrinsinc and endogenous noise sources, thus generalizing the mean-field formulation introduced in [E. Montbrió et al., Phys. Rev. X 5, 021028 (2015)].

arXiv comment10 pages (with supplementary materials), 3 figures

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• Hierarchy of exact low-dimensional reductions for populations of coupled oscillators
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• Response Theory Identifies Reaction Coordinates and Explains Critical Phenomena in Noisy Interacting Systems
• The effects of degree distributions in random networks of Type-I neurons
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