Stability of the dynamics of an asymmetric neural network

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March 2009, 8(2): 655-671. doi: 10.3934/cpaa.2009.8.655

Stability of the dynamics of an asymmetric neural network

Jianfeng Feng ^1, , Mariya Shcherbina ^2, and Brunello Tirozzi ^3,

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 January 2008 Revised June 2008 Published December 2008

Abstract
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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.

Keywords: Limit theorems, excitatory and inhibitory coupling, neural network.

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

Citation: Jianfeng Feng, Mariya Shcherbina, Brunello Tirozzi. Stability of the dynamics of an asymmetric neural network. Communications on Pure & Applied Analysis, 2009, 8 (2) : 655-671. doi: 10.3934/cpaa.2009.8.655

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