Chaos in Random Neural Networks

1988/07/18 by Haim Sompolinsky, A. Crisanti, H.-J. Sommers · 1,108 citations
Computer Science · Neuroscience · Physics and Astronomy · Mathematics · #Neural Networks and Applications #Neural dynamics and brain function #stochastic dynamics and bifurcation #Lyapunov exponent #Chaotic #Physics #Statistical physics #Limit (mathematics) #Nonlinear system #Phase transition #Critical exponent #Mean field theory #Exponent #Phase (matter) #Chaos theory #Mathematical physics #Quantum mechanics #Mathematics #Mathematical analysis #Computer science

paper · doi:10.1103/physrevlett.61.259

published in Physical Review Letters 61(3), 259-262 (American Physical Society)

openalex publication_date 1988/07/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

A continuous-time dynamic model of a network of N nonlinear elements interacting via random asymmetric couplings is studied. A self-consistent mean-field theory, exact in the N\ensuremath→\ensuremath∞ limit, predicts a transition from a stationary phase to a chaotic phase occurring at a critical value of the gain parameter. The autocorrelations of the chaotic flow as well as the maximal Lyapunov exponent are calculated.

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