Effect of Cauchy noise on a network of quadratic integrate-and-fire neurons with non-Cauchy heterogeneities

Abstract

We analyze the dynamics of large networks of pulse-coupled quadratic integrate-and-fire neurons driven by Cauchy noise and non-Cauchy heterogeneous inputs. Two types of heterogeneities defined by families of $q$-Gaussian and flat distributions are considered. Both families are parametrized by an integer $n$, so that as $n$ increases, the first family tends to a normal distribution, and the second tends to a uniform distribution. For both families, exact systems of mean-field equations are derived and their bifurcation analysis is carried out. We show that noise and heterogeneity can have qualitatively different effects on the collective dynamics of neurons.

arXiv comment9 pages, 5 figures

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• Low-dimensional model for adaptive networks of spiking neurons
• Nonlinear bias of collective oscillation frequency induced by asymmetric Cauchy noise
• Fluctuation induced intermittent transitions between distinct rhythms in balanced excitatory-inhibitory spiking networks
• Two-phase quadratic integrate-and-fire neurons: Exact low-dimensional description for ensembles of finite-voltage neurons