La biforcazione di Hopf e la sua applicazione in alcuni modelli neurali

This thesis shows the basic concepts of bifurcation theory in continuous time dynamical systems. In the first part, it emphasizes the Hopf bifurcation and the stability analysis of the limit cycle in planar systems with the first Lyapunov coefficient's computation. In the second part, it provides an introduction to physical and chemical processes involved in the generation and propagation of action potentials in a neuron. These phenomena are required for the derivation of the classical Hodgkin‐Huxley model. Then, the thesis focuses on the analysis of the two‐dimensional models reduced with the "separation of time scale". Finally, it is performed an analysis of the Hopf bifurcation in neuron models with a discontinuous "frequency‐current" curve, which are called type II neuron models.