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.

9 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