The Kuramoto Model as a Paradigm for Synchronization in Neural Systems

Complex systems - composed of many microscopic interacting units - are characterized by the emergence of self-organized dynamical patterns at the macroscopic level. In particular, synchronization is among the most commonly observed ways of self-organization in biology and physics. This thesis investigates the Kuramoto model, a mathematical framework for describing the onset of synchronization in large populations of coupled oscillators. The first part of this thesis presents a theoretical analysis of the model in the mean-field limit, deriving the critical coupling strength at which the incoherent state loses stability and synchronization appears. The nature of the associated bifurcation is also discussed. These analytical results are supported by numerical simulations illustrating the system’s behavior across different dynamical regimes. In the second part, the focus shifts on the relevance of Kuramoto-type models in the study of neuronal synchronization, showing how they can be used to interpret collective oscillatory activity in the brain and to connect microscopic neuronal dynamics with macroscopic observables.