Julien Petit (Ecole Royale Militaire – UNamur)

Title : Peculiarities of reaction and diffusion on temporal networks

Abstract: A common assumption in the ever-increasing literature on network-defined dynamical systems is to view the underlying graph as a static entity. In many cases however, the temporal properties of the network – its fluctuating links and appearing and vanishing nodes –  prove critical.

This presentation is firstly meant as an overview of linear (diffusion) processes on temporal networks. After a survey of recent methods and results, we subsequently focus on a random walk model with lasting node-to-node interactions. Relying on analytics and numerics, we discuss how the Markov property of the process is lost even when using memoryless probability distributions for the model-driven edges dynamics, and the independent nodes processes.

If time permits and in an attempt to highlight other results about systems evolving on top of temporal networks, and which stem from the intrinsic network dynamics, we finally consider a generic nonlinear model. In particular, this setting allows us to discuss pattern formation and oscillations death in reaction-diffusion systems through the Turing mechanism, under the assumption of a fast-varying periodic topology.