A journey in the zoo of Turing patterns: the topology does matter

Description

Spatially non-homogenous states (patterns) can spontaneously emerge in a multitude of Natural of human made systems. In many cases of interest, the interplay between nonlinearities and diffusion seeds a symmetry breaking instability (discovered by Turing in his pioneering work on morphogenesis) that opens the way for the emergence of a rich gallery of patchy motifs. In many relevant cases, distinct populations often interact via an intricate architecture of nested couplings, which can be adequately represented as complex heterogeneous networks. Understanding the patterns onset for networked reaction-diffusion systems is thus a major challenge. In several realms of application, the underlying networks are not composed by a single layer but instead by several ones. Prototypical examples are transportation networks, where agents can use flight, trains, cars, underground, etc… with their applications to epidemic spreading.
In this talk, we consider the process of patterns formation for reaction-diffusion systems anchored on such kind of networks. The framework we propose is general enough as to include multiplex networks as well as multigraphs (i.e. two nodes cane be connected by more than one link).
Interestingly enough, our formalism is able to show the formation destruction) of patchy solution as the number of layers increases and the control of patterns by acting on the network links.

Period	8 Mar 2018
Held at	SMART Infrastructure Facility, Australia, New South Wales
Degree of Recognition	International