The observed patterns that result from the communication between the neurons is very rich: they can notably reveal phenomena of synchronization of neuron discharges which are more or less rhythmic within a population, or phenomena of propagation of waves of neuron discharges in the brain. One of the major questions that will be tackled is to understand what may be the mechanisms underlying all these interesting observations and how to give them the most rigorous mathematical framework possible. Would this result from the intrinsic dynamics of each neuron? From memory effects or learning?. From the spatial complexity of interconnections between neurons? What is the influence of noise ?