MEAN-FIELD ANALYSIS FOR MODEL-BASED SPIKING NETWORKS

The human brain is composed of millions of neurons, firing spikes according to their membrane potentials. The difficulty in studying the brain exists partly because of the randomness property of neurons firing in a network. To understand more about the dynamics of a neuron’s firing rate, we choose to study a specific set of nonlinear dynamical equations that represent a neural network based on a spiking point of view with adaptation qualities. The dynamic membrane potential of a single neuron is a challenge to study since we can hardly know the number of spikes fired at a certain time. In this thesis, we use phase-plane analysis and more precisely mean-field analysis to address the random nature of the dynamic of model-based spiking networks. We find that the dynamics of neurons in a network offer exploitable and relevant information such as patterns of stable or unstable oscillations in certain circumstances