Eur. Phys. J. B (2016) 89: 260
https://doi.org/10.1140/epjb/e2016-70248-6

Regular Article

Tune the topology to create or destroy patterns

¹ naXys, Namur Center for Complex Systems, University of Namur, rempart de la Vierge 8, B 5000 Namur, Belgium
² Dipartimento di Fisica e Astronomia, University of Florence, INFN and CSDC, via Sansone 1, 50019 Sesto Fiorentino, Florence, Italy

^a e-mail: malbor.asllani@unamur.be

Received: 24 April 2016
Received in final form: 5 September 2016
Published online: 5 December 2016

Abstract

We consider the dynamics of a reaction-diffusion system on a multigraph. The species share the same set of nodes but can access different links to explore the embedding spatial support. By acting on the topology of the networks we can control the ability of the system to self-organise in macroscopic patterns, emerging as a symmetry breaking instability of an homogeneous fixed point. Two different cases study are considered: on the one side, we produce a global modification of the networks, starting from the limiting setting where species are hosted on the same graph. On the other, we consider the effect of inserting just one additional single link to differentiate the two graphs. In both cases, patterns can be generated or destroyed, as follows the imposed, small, topological perturbation. Approximate analytical formulae allow to grasp the essence of the phenomenon and can potentially inspire innovative control strategies to shape the macroscopic dynamics on multigraph networks.