Exact low-dimensional description for fast neural oscillations with low firing rates

Abstract

Recently, low-dimensional models of neuronal activity have been exactly derived for large networks of deterministic, Quadratic Integrate-and-Fire (QIF) neurons. Such firing rate models (FRM) describe the emergence of fast collective oscillations (>30~Hz) via the frequency-locking of a subset of neurons to the global oscillation frequency. However, the suitability of such models to describe realistic neuronal states is seriously challenged by fact that during episodes of fast collective oscillations, neuronal discharges are often very irregular and have low firing rates compared to the global oscillation frequency. Here we extend the theory to derive exact FRM for QIF neurons to include noise, and show that networks of stochastic neurons displaying irregular discharges at low firing rates during episodes of fast oscillations, are governed by exactly the same evolution equations as deterministic networks. Our results reconcile two traditionally confronted views on neuronal synchronization, and upgrade the applicability of exact FRM to describe a broad range of biologically realistic neuronal states.

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Cited by in corpus (7)

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• Low Dimensional Dynamics of Globally Coupled Complex Riccati Equations: Exact Firing-rate Equations for Spiking Neurons with Clustered Substructure
• Coexistence of asynchronous and clustered dynamics in noisy inhibitory neural networks
• Two-phase quadratic integrate-and-fire neurons: Exact low-dimensional description for ensembles of finite-voltage neurons
• Impact of heavy-tailed synaptic strength distributions on self-sustained activity in networks of spiking neurons
• Phase transformation and synchrony for a network of coupled Izhikevich neurons