title: Optimal system size for complex dynamics in random neural networks near criticality.
abstract: In this article, we consider a model of dynamical agents coupled through a random connectivity matrix, as introduced by Sompolinsky et al. [Phys. Rev. Lett. 61(3), 259-262 (1988)] in the context of random neural networks. When system size is infinite, 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 sub-critical regime for finite size systems: 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.
authors.affiliation: Laboratoire Analyse Géométrie et Applications, Université Paris XIII, Villetaneuse, France.
authors.forename: Gilles
authors.initials: G
authors.lastname: Wainrib
authors.affiliation: Institute Jacques Monod, Université Paris VII, Paris, France.
authors.forename: Luis Carlos
authors.initials: LC
authors.lastname: García del Molino
mesh_terms: D008959:Models, Neurological; D016571:Neural Networks, Computer