  In 2018, Ferrari et al. wrote a paper called "Phase Transition for Infinite
Systems of Spiking Neurons" in which they introduced a continuous time
stochastic model of interacting neurons. This model has a parameter $\gamma$,
corresponding to the rate of the leaking times of the neurons and, as the title
says, it was proven there to present a phase transition phenomenon with respect
to this $\gamma$. Here we prove that this model also exhibit a metastable
behavior. By this we mean that if $\gamma$ is small enough, then the
re-normalized time of extinction converges toward an exponential random
variable of mean 1 as the number of neurons goes to infinity.
