A Minimal Network of Brain Dynamics: Hierarchy of Approximations to Quasi-critical Neural Network Dynamics

2025/12/26 by Jeremy B. Goetz, Jeremy Goetz, Goetz, Jeremy B. +9
Neuroscience · Physics and Astronomy · Computer Science · #Neural dynamics and brain function #stochastic dynamics and bifurcation #Neural Networks and Applications

paper · pdf · doi:10.48550/arxiv.2512.22093

Abstract

We present an interacting model of neural network dynamics that incorporates key biological features, including multiple forms of inhibitory interactions. We develop a hierarchy of analytical mean-field approximations to characterize nonequilibrium phase transitions between ordered, disordered, and chaotic regimes, complemented by a detailed stability analysis. We show that inhibition generically enhances the stability of network dynamics. The model is consistent with the quasi-criticality hypothesis, exhibiting regions of maximal dynamical susceptibility and mutual information, modulated by the strength of external stimuli. We further demonstrate that, at the mean-field level, the critical transition belongs to the mean-field directed percolation universality class, in agreement with prior experimental and theoretical studies. More broadly, our framework may offer insights into neurological disorders, with the unstable regime exhibiting chaotic dynamics that may be associated with epileptic seizures.

Citations

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