Communications on Pure and Applied Analysis (CPAA)

Stability of the dynamics of an asymmetric neural network

Pages: 655 - 671, Volume 8, Issue 2, March 2009      doi:10.3934/cpaa.2009.8.655

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Jianfeng Feng - Department of Computer Science and Mathematics, Warwick University, Coventry CV4 7AL, United Kingdom (email)
Mariya Shcherbina - Institute for Low Temperature Physics, Lenin ave 47, 61103, Ukraine (email)
Brunello Tirozzi - Department of Physics, Rome Univ. "La Sapienza", P. Aldo Moro 5, 00185 Roma, Italy (email)

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.

Keywords:  Limit theorems, excitatory and inhibitory coupling, neural network
Mathematics Subject Classification:  Primary: 60-xx, 93-xx; Secondary: 93Dxx

Received: January 2008;      Revised: June 2008;      Available Online: December 2008.