Formazione di pattern su reti con differenti topologie

Pattern formation is ubiquitous in Nature. It plays a significant role in a variety of systems, such as in vegetation organization, clouds distribution, and the formation of sand ripples. Because of its universality, several fields of science have studied it, especially in continuous media. Recently, the growing interest in Graph theory has led to applying it also on complex networks. The Swift-Hohenberg model is one of the most canonical instruments used in pattern formation, it is the pillar of this work thanks to its versatility and its simplicity. The aim of this thesis is studying through numerical simulations what happens to the SH model when the topology is slowly transformed from a 2D regular lattice to a complex network.