Critical and resonance phenomena in neural networks

TL;DR

This paper investigates how neural networks exhibit critical and resonance phenomena leading to brain rhythms, revealing phase transitions influenced by noise, network structure, and excitation-inhibition balance, with implications for understanding brain dynamics.

Contribution

It introduces an analytical and simulation-based study of critical phenomena and resonance in neural networks, highlighting the role of phase transitions in brain rhythm emergence.

Findings

Network oscillations emerge at a critical noise level.

Relaxation time and response are maximized near the critical point.

Damped oscillations and fluctuations intensify approaching the transition.

Abstract

Brain rhythms contribute to every aspect of brain function. Here, we study critical and resonance phenomena that precede the emergence of brain rhythms. Using an analytical approach and simulations of a cortical circuit model of neural networks with stochastic neurons in the presence of noise, we show that spontaneous appearance of network oscillations occurs as a dynamical (non-equilibrium) phase transition at a critical point determined by the noise level, network structure, the balance between excitatory and inhibitory neurons, and other parameters. We find that the relaxation time of neural activity to a steady state, response to periodic stimuli at the frequency of the oscillations, amplitude of damped oscillations, and stochastic fluctuations of neural activity are dramatically increased when approaching the critical point of the transition.