Turing patterns on time varying networks

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 static but rather evolve over time; the couplings are created, destroyed, or rewired as time goes on. Prototypical examples are contact networks with their applications to epidemic spreading. In this talk, we consider the process of patterns formation for reaction-diffusion systems anchored on networks that evolve over time. The framework we propose is general enough as to include networks that are periodically rearranged in time (both in a continuous or discontinuous way), but also nonperiodic or even stochastic time varying networks. Interestingly enough, our formalism is able to describe the oscillation death phenomenon, i.e. the possibility for an initially synchronized state to evolve towards an asymptotic inhomogeneous steady configuration, in response to an externally
injected perturbation.

Period	1 Mar 2018
Held at	University of South Wales, Australia
Degree of Recognition	International