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Flow version of statistical neurodynamics for oscillator neural networks

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  • Uchiyama, Satoki

Abstract

We consider a neural network of Stuart–Landau oscillators as an associative memory. This oscillator network with N elements is a system of an N-dimensional differential equation, works as an attractor neural network, and is expected to have no Lyapunov functions. Therefore, the technique of equilibrium statistical physics is not applicable to the study of this system in the thermodynamic limit. However, the simplicity of this system allows us to extend statistical neurodynamics [S. Amari, K. Maginu, Neural Netw. 1 (1988) 63–73], which was originally developed to analyse the discrete time evolution of the Hopfield model, into the version for continuous time evolution. We have developed and attempted to apply this method in the analysis of the phase transition of our model network.

Suggested Citation

  • Uchiyama, Satoki, 2012. "Flow version of statistical neurodynamics for oscillator neural networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(8), pages 2807-2817.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:8:p:2807-2817
    DOI: 10.1016/j.physa.2011.12.026
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    Cited by:

    1. Hemmat Esfe, Mohammad & Rostamian, Hossein & Esfandeh, Saeed & Afrand, Masoud, 2018. "Modeling and prediction of rheological behavior of Al2O3-MWCNT/5W50 hybrid nano-lubricant by artificial neural network using experimental data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 625-634.

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