# American Institute of Mathematical Sciences

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

## 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  January 2008 Revised  June 2008 Published  December 2008

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