On the relationship between equilibria and dynamics in large, random neuronal networks

Xiaoyu Yang; Giancarlo La Camera; Gianluigi Mongillo

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arXiv · 2510.19091

On the relationship between equilibria and dynamics in large, random neuronal networks

Xiaoyu Yang·Giancarlo La Camera·Gianluigi Mongillo

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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 an extensive, but fractionally-small, number of unstable directions. Despite network's connectivity being completely random, the equilibria are strongly correlated and, as a result, they occupy a small region in the phase space. The attractor is inside this region. This geometry explains why the chaotic dynamics in these models can be described by a fractionally-small number of collective modes.

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Xiaoyu Yang, Giancarlo La Camera, Gianluigi Mongillo. 2025-10-21. On the relationship between equilibria and dynamics in large, random neuronal networks. https://arxiv.org/abs/2510.19091

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