Tune the topology to create or destroy patterns

TL;DR

This paper investigates how changing the topology of multigraph networks can control the emergence or destruction of spatial patterns in reaction-diffusion systems, offering analytical insights for network-based pattern control.

Contribution

It introduces a method to manipulate pattern formation by topological modifications in multigraph networks, including global changes and single-link insertions, supported by analytical formulas.

Findings

Topology modifications can induce or suppress patterns.

Single-link perturbations significantly affect system dynamics.

Analytical formulas explain the impact of topological changes.

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 allows to grasp the essence of the phenomenon and can potentially inspire innovative control strategies to shape the macroscopic dynamics on multigraph networks