Macroscopic dynamics of quadratic integrate-and-fire neurons subject to correlated noise

TL;DR

This paper develops a mean-field model for quadratic integrate-and-fire neurons influenced by correlated Gaussian noise, revealing that increased noise correlation suppresses activity and induces metastable state transitions, advancing understanding of neural population dynamics.

Contribution

It introduces a reduced mean-field framework for correlated noise in quadratic integrate-and-fire neurons, highlighting counterintuitive activity suppression and metastability phenomena.

Findings

Increased noise correlation suppresses network activity.

The network exhibits metastability with spontaneous state transitions.

The model accurately captures population dynamics under correlated noise.

Abstract

The presence of correlated noise, arising from a mixture of independent fluctuations and a common noisy input shared across the neural population, is a ubiquitous feature of neural circuits, yet its impact on collective network dynamics remains poorly understood. We analyze a network of quadratic integrate-and-fire neurons driven by Gaussian noise with a tunable degree of correlation. Using the cumulant expansion method, we derive a reduced set of effective mean-field equations that accurately describe the evolution of the population's mean firing rate and membrane potential. Our analysis reveals a counterintuitive phenomenon: increasing the noise correlation strength suppresses the mean network activity, an effect we term correlated-noise-inhibited spiking. Furthermore, within a specific parameter regime, the network exhibits metastability, manifesting itself as spontaneous, noise-driven transitions between distinct high- and low-activity states. These results provide a theoretical framework for reducing the dynamics of complex stochastic networks and demonstrate how correlated noise can fundamentally regulate macroscopic neural activity, with implications for understanding state transitions in biological systems.