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

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.

11 pages, 2 figures

References in corpus (3)

• Dynamical synapses causing self-organized criticality in neural networks
• Topological and Dynamical Complexity of Random Neural Networks
• Extremal laws for the real Ginibre ensemble

Cited by in corpus (1)

• Regular graphs maximize the variability of random neural networks