The Blume–Emery–Griffiths neural network: dynamics for arbitrary temperature

D. Bollé, J.Busquets Blanco, G.M. Shim and T. Verbeiren

Physica A: Statistical Mechanics and its Applications, 2004, vol. 331, issue 1, 319-350

Abstract: The parallel dynamics of the fully connected Blume–Emery–Griffiths neural network model is studied for arbitrary temperature. By employing a probabilistic signal-to-noise approach, a recursive scheme is found determining the time evolution of the distribution of the local fields and, hence, the evolution of the order parameters. A comparison of this approach is made with the generating functional method, allowing to calculate any physical relevant quantity as a function of time. Explicit analytic formula are given in both methods for the first few time steps of the dynamics. Up to the third time step the results are identical. Some arguments are presented why beyond the third time step the results differ for certain values of the model parameters. Furthermore, fixed-point equations are derived in the stationary limit. Numerical simulations confirm our theoretical findings.

Keywords: Parallel dynamics; Fully connected networks; Probabilistic approach; Generating functional approach; Thermal fields (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:331:y:2004:i:1:p:319-350

DOI: 10.1016/S0378-4371(03)00629-0

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