During my undergraduate studies at the University of Florence, in Theoretical Physics, I attended courses mainly in Statistical Mechanics, Applied Mathematics and Fundamental Physics. In 2009, during my master thesis and, later, during my PhD (2010-2012), I implemented analytical and numerical methods borrowed from nonlinear dynamics to study complex networks such as pulse-coupled neural networks with different topologies. In particular I used simple mathematical models to describe neural network dynamics and nonlinear data analysis tools to characterize the emergent collective dynamics.
The main aims of my PhD research were: (1) to investigate the role played by the topology in promoting coherent activity in pulse-coupled networks; (2) to understand if the onset of collective oscillations can be related to a minimal average connectivity and how this critical connectivity depends on the size of the networks; (3) to characterize the degree of chaoticity of these networks; (4) to investigate the emergence of peculiar states (e.g. collective chaos, chimera states) in neural networks; (5) to give general criteria for the stability of the “splay state” (asynchronous state) for oscillators (neurons) with generic velocity fields.
Afterwards, during my first postdoc fellowship (2012-2014) and later during my fixed term position as researcher, I started working on dynamical models of power grids, focusing my attention on complex phase models and multiscale networks. In particular, I have studied models of phase coupled oscillators with inertia, which have been initially introduced to mimic the synchronization mechanisms observed among the fireflies Pteroptix Malaccae and, more recently, employed also to investigate the self-synchronization in power grids. In particular, I have performed finite size numerical investigations and mean field thoretical analysis of a Kuramoto model with inertia for fully coupled and diluted systems. In this regards, I examined, from a dynamical point of view, the hysteretic transition from incoherence to coherence for increasingly large system size and inertia, thus characterizing the synchronization properties of the system. This period has been proved effective to enable me to learn fundamental theoretical tools such as the reduction to collective variables and acquire new knowledge in network theory from a multidisciplinary perspective.