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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:
 [1]
  1. Laboratoire Analyse Géométrie et Applications, Université Paris XIII, Villetaneuse (France)
Publication Date:
OSTI Identifier:
22251731
Resource Type:
Journal Article
Journal Name:
Chaos (Woodbury, N. Y.)
Additional Journal Information:
Journal Volume: 23; Journal Issue: 4; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1054-1500
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

Citation Formats

Wainrib, Gilles, and García del Molino, Luis Carlos, E-mail: garciadelmolino@ijm.univ-paris-diderot.fr. Optimal system size for complex dynamics in random neural networks near criticality. United States: N. p., 2013. Web. doi:10.1063/1.4841396.
Wainrib, Gilles, & García del Molino, Luis Carlos, E-mail: garciadelmolino@ijm.univ-paris-diderot.fr. Optimal system size for complex dynamics in random neural networks near criticality. United States. https://doi.org/10.1063/1.4841396
Wainrib, Gilles, and García del Molino, Luis Carlos, E-mail: garciadelmolino@ijm.univ-paris-diderot.fr. 2013. "Optimal system size for complex dynamics in random neural networks near criticality". United States. https://doi.org/10.1063/1.4841396.
@article{osti_22251731,
title = {Optimal system size for complex dynamics in random neural networks near criticality},
author = {Wainrib, Gilles and García del Molino, Luis Carlos, E-mail: garciadelmolino@ijm.univ-paris-diderot.fr},
abstractNote = {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.},
doi = {10.1063/1.4841396},
url = {https://www.osti.gov/biblio/22251731}, journal = {Chaos (Woodbury, N. Y.)},
issn = {1054-1500},
number = 4,
volume = 23,
place = {United States},
year = {Sun Dec 15 00:00:00 EST 2013},
month = {Sun Dec 15 00:00:00 EST 2013}
}