American Institute of Mathematical Sciences

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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

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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