Stability of the dynamics of an asymmetric neural network

2006/12/01 by J. F. Feng, Feng, J. F., M. Shcherbina +3
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Statistics Theory (math.ST) #math-ph #math.MP #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.math-ph/0612006

17 pages

arxiv created 2006/12/01 · arxiv updated 2011/11/10

Abstract

We study the stability of the dynamics of a network of n neurons intercting linearly through a random gaussian matrix of excitatory and inhibitory type. Using the aproach developed in a previous paper we show some interesting properties of the dynamic of this system for large values of n. We got sufficient conditions for getting diverging synchronized behavior or stability.

Related

• Stability of synchronous states in sparse neuronal networks
• Asymptotic behavior of a network of neurons with random linear interactions
• Asymptotic description of stochastic neural networks. I - existence of a Large Deviation Principle
• Pattern Storage, Bifurcations and Higher-Order Correlation Structure of an Exactly Solvable Asymmetric Neural Network Model
• On the dynamics of random neuronal networks