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.
@article{arxiv.1301.3779,
title = {Optimal system size for complex dynamics in random neural networks near criticality},
author = {Gilles Wainrib and Luis Carlos García del Molino},
journal= {arXiv preprint arXiv:1301.3779},
year = {2015}
}