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

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.