Stability of the dynamics of an asymmetric neural network

Jianfeng Feng; Mariya Shcherbina; Brunello Tirozzi

doi:10.3934/cpaa.2009.8.655

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2009, Volume 8, Issue 2: 655-671. Doi: 10.3934/cpaa.2009.8.655

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Stability of the dynamics of an asymmetric neural network

1.
Department of Computer Science and Mathematics, Warwick University, Coventry CV4 7AL
2.
Institute for Low Temperature Physics, Lenin ave 47, 61103
3.
Department of Physics, Rome Univ. "La Sapienza", P. Aldo Moro 5, 00185 Roma

Received: December 31, 2007

Revised: May 31, 2008

Published: February 2009

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Abstract

We study the stability of the dynamics of a network of $n$ formal neurons interacting through an asymmetric matrix with independent random Gaussian elements of the type introduced by Rajan and Abbott ([1]). The neurons are represented by the values of their electric potentials $x_i, i=1,\cdots,n$. Using the approach developed in a previous paper by us ([6]) we obtain sufficient conditions for diverging synchronized behavior and for stability.

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Mathematics Subject Classification: Primary: 60-xx, 93-xx; Secondary: 93Dxx.

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