Before revision:  We study mathematically these Markov chains and obtain a lower bound on the number of external stimulus that the network can receive before the initial signal is URLotten .
After revision:  We study mathematically these Markov chains and obtain a lower bound on the number of external stimulus that the network can receive before the initial signal is considered as URLotten (probability of error above a given threshold). Our results hold for finite size networks as well as in the large size asymptotic. They are based on a finite time analysis rather than large time asymptotic .