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

Abstract

Cortical neural circuits display highly irregular spiking in individual neurons but variably sized collective firing, oscillations and critical avalanches at the population level, all of which have functional importance for information processing. Theoretically, the balance of excitation and inhibition inputs is thought to account for spiking irregularity and critical avalanches may originate from an underlying phase transition. However, the theoretical reconciliation of these multilevel dynamic aspects in neural circuits remains an open question. Herein, we study excitation-inhibition (E-I) balanced neuronal network with biologically realistic synaptic kinetics. It can maintain irregular spiking dynamics with different levels of synchrony and critical avalanches emerge near the synchronous transition point. We propose a novel semi-analytical mean-field theory to derive the field equations governing the network macroscopic dynamics. It reveals that the E-I balanced state of the network manifesting irregular individual spiking is characterized by a macroscopic stable state, which can be either a fixed point or a periodic motion and the transition is predicted by a Hopf bifurcation in the macroscopic field. Furthermore, by analyzing public data, we find the coexistence of irregular spiking and critical avalanches in the spontaneous spiking activities of mouse cortical slice in vitro, indicating the universality of the observed phenomena. Our theory unveils the mechanism that permits complex neural activities in different spatiotemporal scales to coexist and elucidates a possible origin of the criticality of neural systems. It also provides a novel tool for analyzing the macroscopic dynamics of E-I balanced networks and its relationship to the microscopic counterparts, which can be useful for large-scale modeling and computation of cortical dynamics.

References in corpus (18)

• Weak pairwise correlations imply strongly correlated network states in a neural population
• Crackling Noise
• Optimal Dynamical Range of Excitable Networks at Criticality
• Dynamical synapses causing self-organized criticality in neural networks
• Brain organization into resting state networks emerges at criticality on a model of the human connectome
• Macroscopic description for networks of spiking neurons
• Power-law statistics and universal scaling in the absence of criticality
• Landau-Ginzburg theory of cortex dynamics: Scale-free avalanches emerge at the edge of synchronization
• Towards a theory of cortical columns: From spiking neurons to interacting neural populations of finite size
• Control of criticality and computation in spiking neuromorphic networks with plasticity
• Between perfectly critical and fully irregular: a reverberating model captures and predicts cortical spike propagation
• Low-dimensional spike rate models derived from networks of adaptive integrate-and-fire neurons: Comparison and implementation
• Macroscopic phase resetting-curves determine oscillatory coherence and signal transfer in inter-coupled neural circuits
• Neutral theory and scale-free neural dynamics
• A simple unified view of branching process statistics: random walks in balanced logarithmic potentials
• How strong are correlations in strongly recurrent neuronal networks?
• Unveiling causal activity of complex networks
• A general mechanism for the `$1/f$' noise

Cited by in corpus (5)

• Hybrid-type synchronization transitions: where marginal coherence, scale-free avalanches, and bistability live together
• Less is More: Wiring-Economical Modular Networks Support Self-Sustained Firing-Economical Neural Avalanches for Efficient Processing
• Criticality in Reservoir Computer of Coupled Phase Oscillators
• Synchronization transitions on connectome graphs with external force
• Sandpile cascades on oscillator networks: the BTW model meets Kuramoto