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

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:
 [1] ;  [2]
  1. Laboratoire Analyse Géométrie et Applications, Université Paris XIII, Villetaneuse (France)
  2. Institute Jacques Monod, Université Paris VII, Paris (France)
Publication Date:
OSTI Identifier:
22251239
Resource Type:
Journal Article
Resource Relation:
Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 23; Journal Issue: 4; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CHAOS THEORY; EIGENVALUES; MATRICES; NEURAL NETWORKS; PHASE TRANSFORMATIONS; PROBABILITY; RANDOMNESS