We study a continuous-time stochastic system of spiking neurons from the perspective of phase transition and metastability, using mathematical concepts and techniques borrowed from statistical physics. The model we consider is a continuous-time version of the Galves-Löcherbach model, in which the interaction beetwen the components is given by the one-dimensional lattice. It has already been proven to be subject to a phase transition with respect to the leakage parameter. In this work we show that the system is metastable in one of the phase, while it is not in the other. We then consider the same model with different graphs of interaction and we obtain various results of phase transition and mestability.

Nessa tese, estudamos um sistema estocástico em tempo continuo de neurônios gerando disparos, do ponto de vista dos fenômenos de transição de fase e de metaestabilidade, usando conceitos matemáticos e técnicas emprestado da física estatística.