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Cortical neural circuits display highly irregular spiking in individualneurons but variably sized collective firing, oscillations and criticalavalanches at the population level, all of which have functional importance forinformation processing. Theoretically, the balance of excitation and inhibitioninputs is thought to account for spiking irregularity and critical avalanchesmay originate from an underlying phase transition. However, the theoreticalreconciliation of these multilevel dynamic aspects in neural circuits remainsan open question. Herein, we study excitation-inhibition (E-I) balancedneuronal network with biologically realistic synaptic kinetics. It can maintainirregular spiking dynamics with different levels of synchrony and criticalavalanches emerge near the synchronous transition point. We propose a novelsemi-analytical mean-field theory to derive the field equations governing thenetwork macroscopic dynamics. It reveals that the E-I balanced state of thenetwork manifesting irregular individual spiking is characterized by amacroscopic stable state, which can be either a fixed point or a periodicmotion and the transition is predicted by a Hopf bifurcation in the macroscopicfield. Furthermore, by analyzing public data, we find the coexistence ofirregular spiking and critical avalanches in the spontaneous spiking activitiesof mouse cortical slice in vitro, indicating the universality of the observedphenomena. Our theory unveils the mechanism that permits complex neuralactivities in different spatiotemporal scales to coexist and elucidates apossible origin of the criticality of neural systems. It also provides a noveltool for analyzing the macroscopic dynamics of E-I balanced networks and itsrelationship to the microscopic counterparts, which can be useful forlarge-scale modeling and computation of cortical dynamics.

frontiers in systems neuroscience

Hopf Bifurcation in Mean Field Explains Critical Avalanches in  Excitation-Inhibition Balanced Neuronal Networks: A Mechanism for Multiscale  Variability