On the relationship between equilibria and dynamics in large, random neuronal networks
Disordered Systems and Neural Networks
2025-10-23 v1
Abstract
We investigate the equilibria of a random model network exhibiting extensive chaos. In this regime, a large number of equilibria is present. They are all saddles with low-dimensional unstable manifolds. Surprisingly, despite network's connectivity being completely random, the equilibria are strongly correlated and, as a result, they occupy a very small region in the phase space. The attractor is inside this region. This geometry explains why the collective states sampled by the dynamics are dominated by correlation effects and, hence, why the chaotic dynamics in these models can be described by a fractionally-small number of collective modes.
Cite
@article{arxiv.2510.19091,
title = {On the relationship between equilibria and dynamics in large, random neuronal networks},
author = {Xiaoyu Yang and Giancarlo La Camera and Gianluigi Mongillo},
journal= {arXiv preprint arXiv:2510.19091},
year = {2025}
}