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 approach of Dai we use the fluid limit model of the network to derive a sufficient condition for positive Harris-recurrence of the associated Markov process. This improves the main result in Karpelevich et al. and, at the same time, sheds some new light on it. We further derive two different conditions that are sufficient for transience of the state process and illustrate our results by classifying some examples according to positive recurrence or transience.