Recurrence and transience properties of some neural networks: an approach via fluid limit models

The subject of the paper is the stability analysis of some neural networks consisting of a finite number of interacting neurons. Following the approac h of Dai [5] we use the fluid limit model of the network to derive a suffic ient condition for positive Harris-recurrence of the associated Markov proc ess. This improves the main result in Karpelevich et al. [11] and, at the s ame time, sheds some new light on it. We further derive two different condi tions that are sufficient for transience of the state process and illustrat e our results by classifying some examples according to positive recurrence or transience.