Optimal system size for complex dynamics in random neural networks near criticality

TL;DR

This paper investigates how the likelihood of complex, chaotic dynamics in random neural networks peaks at an optimal intermediate system size near the critical point, explained through eigenvalue extreme value theory.

Contribution

It reveals a novel system size resonance phenomenon in the subcritical regime of random neural networks near criticality, supported by eigenvalue analysis.

Findings

Maximum probability of complex dynamics at intermediate system size near criticality

System size resonance explained by extreme eigenvalue statistics

Chaotic behavior peaks in the subcritical regime close to phase transition

Abstract

In this Letter, we consider a model of dynamical agents coupled through a random connectivity matrix, as introduced in [Sompolinsky et. al, 1988] in the context of random neural networks. It is known that increasing the disorder parameter induces a phase transition leading to chaotic dynamics. We observe and investigate here a novel phenomenon in the subcritical regime : the probability of observing complex dynamics is maximal for an intermediate system size when the disorder is close enough to criticality. We give a more general explanation of this type of system size resonance in the framework of extreme values theory for eigenvalues of random matrices.