F. A. Galymanov, F. M. Gafarov, N. R. Khusnutdinov, “Neural network growths model”, Mat. Model., 23:3 (2011), 101

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Matematicheskoe modelirovanie, 2011, Volume 23, Number 3, Pages 101–108 (Mi mm3090)

Neural network growths model

F. A. Galymanov^a, F. M. Gafarov^a, N. R. Khusnutdinov^b

^a Tatar State University of Humanity and Pedagogic, Department of Physics, Kazan, Russia
^b Kazan State University, Department of Physics, Kazan, Russia

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Abstract: The dynamical model of the biological neurons net creation is suggested. The dynamics of growth of the net is described by standard heat equation with activity neurons equation. The footing of the theory is very simple – the axon growth is in the direction of the greatest media concentration which supply its growth. The media is standing out by neurons in active state. The activation takes place due to external random influences. The system of equations is solved for two dimensional as well as three dimensional cases.

Keywords: neural networks, diffusion equation, neural network's plasticity, axon growth.

Received: 05.04.2010

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Document Type: Article

Language: Russian

Citation: F. A. Galymanov, F. M. Gafarov, N. R. Khusnutdinov, “Neural network growths model”, Mat. Model., 23:3 (2011), 101–108

Citation in format AMSBIB

\Bibitem{GalGafKhu11}

\by F.~A.~Galymanov, F.~M.~Gafarov, N.~R.~Khusnutdinov

\paper Neural network growths model

\jour Mat. Model.

\yr 2011

\vol 23

\issue 3

\pages 101--108

\mathnet{http://mi.mathnet.ru/mm3090}

\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=2849300}

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