Coherent oscillations in balanced neural networks driven by endogenous fluctuations

TL;DR

This paper analyzes how balanced neural networks with quadratic integrate-and-fire neurons exhibit either asynchronous activity or periodic oscillations, using mean field models and simulations to understand the underlying dynamics and effects of heterogeneity.

Contribution

It provides a detailed analysis of dynamical regimes in balanced neural networks, introducing a mean field model that accurately captures oscillations and the influence of heterogeneity.

Findings

Mean field models reproduce asynchronous and oscillatory regimes.

Heterogeneity influences the emergence of collective oscillations.

Low-dimensional reduction captures transition scenarios.

Abstract

We present a detailed analysis of the dynamical regimes observed in a balanced network of identical Quadratic Integrate-and-Fire (QIF) neurons with a sparse connectivity for homogeneous and heterogeneous in-degree distribution. Depending on the parameter values, either an asynchronous regime or periodic oscillations spontaneously emerge. Numerical simulations are compared with a mean field model based on a self-consistent Fokker-Planck equation (FPE). The FPE reproduces quite well the asynchronous dynamics in the homogeneous case by either assuming a Poissonian or renewal distribution for the incoming spike trains. An exact self consistent solution for the mean firing rate obtained in the limit of infinite in-degree allows identifying balanced regimes that can be either mean- or fluctuation-driven. A low-dimensional reduction of the FPE in terms of circular cumulants is also considered. Two cumulants suffice to reproduce the transition scenario observed in the network. The emergence of periodic collective oscillations is well captured both in the homogeneous and heterogeneous setups by the mean field models upon tuning either the connectivity, or the input DC current. In the heterogeneous situation we analyze also the role of structural heterogeneity.