This thesis is devoted to complex systems, more particularly to neural networks. Disassociated in vitro rat brain neuron cultures show, under a variety of experimental contexts, a spontaneous electrical activity. This activity manifests itself by a rapid succession of ignitions of a large fraction of neurons named collective bursts. The study of the initiators of these bursts is one of the conceptual problems underlying the spontaneous electrical activity. A study of Eytan and Marom showed that some "first to fire" cells exist. In this thesis, we study these particular neurons, through a detailed analysis of data obtained by the multi-electrode array methods and simulations. We have established that some cells are triggering bursts beyond a simple statistical effect of being the first. These particular cells are called leaders. The analysis of experimental data indicates that the long term dynamics of the leaders is relatively robust and that these leaders are not only the main initiators of bursts, but, the burst itself carries traces indicating which of the leaders has initiated the burst. The study of simulations using the leaky integrate and fire neuron model permitted us to find out that leaders form naturally from a balanced combination of inputs, outputs, their local neighborhood and their own properties. Basically, a leader is an excitatory neuron, has a low membrane potential firing threshold, sends a signal to a lot of excitatory neurons as well as to a few inhibitory neurons and a leader receives only a few signals from other excitatory neurons.