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Minimal network of brain dynamics: Hierarchy of approximations to quasicritical neural network dynamics

Jeremy B. Goetz1,*, Naruepon Weerawongphrom1,*, Rashid V. Williams-García2, John M. Beggs1, and Gerardo Ortiz1

  • *These authors contributed equally to this work.
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Phys. Rev. E 114, 044321 – Published 22 October, 2026

DOI: https://doi.org/10.1103/64b7-qb8p

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 quasicriticality 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.

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Phys. Rev. E 114, 044321– Published 22 October, 2026
  • Received 26 December 2025
  • Accepted 29 June 2026
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