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Correlations between synapses in pairs of neurons slow down dynamics in randomly connected neural networks

Daniel Martí, Nicolas Brunel, and Srdjan Ostojic
Phys. Rev. E 97, 062314 – Published 26 June 2018

Abstract

Networks of randomly connected neurons are among the most popular models in theoretical neuroscience. The connectivity between neurons in the cortex is however not fully random, the simplest and most prominent deviation from randomness found in experimental data being the overrepresentation of bidirectional connections among pyramidal cells. Using numerical and analytical methods, we investigate the effects of partially symmetric connectivity on the dynamics in networks of rate units. We consider the two dynamical regimes exhibited by random neural networks: the weak-coupling regime, where the firing activity decays to a single fixed point unless the network is stimulated, and the strong-coupling or chaotic regime, characterized by internally generated fluctuating firing rates. In the weak-coupling regime, we compute analytically, for an arbitrary degree of symmetry, the autocorrelation of network activity in the presence of external noise. In the chaotic regime, we perform simulations to determine the timescale of the intrinsic fluctuations. In both cases, symmetry increases the characteristic asymptotic decay time of the autocorrelation function and therefore slows down the dynamics in the network.

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  • Received 28 July 2017
  • Revised 16 May 2018

DOI:https://doi.org/10.1103/PhysRevE.97.062314

©2018 American Physical Society

Physics Subject Headings (PhySH)

Physics of Living SystemsNonlinear DynamicsNetworksStatistical Physics & Thermodynamics

Authors & Affiliations

Daniel Martí1, Nicolas Brunel2,3, and Srdjan Ostojic1

  • 1Laboratoire de Neurosciences Cognitives, Inserm UMR No. 960, Ecole Normale Supérieure, PSL Research University, 75230 Paris, France
  • 2Department of Statistics and Department of Neurobiology, University of Chicago, Chicago, Illinois 60637, USA
  • 3Department of Neurobiology and Department of Physics, Duke University, Durham, North Carolina 27710, USA

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Issue

Vol. 97, Iss. 6 — June 2018

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