Oscillations and diffusion in dynamic networks models
The interconnection of individual systems, whose behaviour is rather simple, can give rise to complicated models with much richer dynamics. Indeed, the study of complex systems has been able to shed some light on phenomena such as synchronisation, patterns, symmetries, and many others.
The objective of Riccardo Bonetto's thesis is to show the interplay between the network structure and the dynamics. To achieve this, Bonetto analyses some relevant models of complex dynamical systems where the interacting components are described by a network. He considers both linear and nonlinear models, including oscillations and diffusion. Bonetto's focus is on the analytical results, which provide a theoretical understanding of relevant properties such as the synchrony patterns, the influence of the network on the dynamical properties, the role of symmetries.
The methods of Bonetto's study span a broad class of mathematics, including algebraic graph theory, perturbation theory, stability and bifurcation theory, and Hamiltonian systems. He also performs numerical simulations, not only to corroborate the findings, but also to explore phenomena such as chaos and spatiotemporal patterns.