Tune the topology to create or destroy patterns

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

11 pages, 6 figures

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Cited by in corpus (9)

• Turing patterns mediated by network topology in homogeneous active systems
• Turing patterns on discrete topologies: from networks to higher-order structures
• The role of modularity in self-organisation dynamics in biological networks
• Emergence of geometric Turing patterns in complex networks
• Turing instability and pattern formation on directed networks
• Effect of clustering on Turing instability in complex networks
• Amplitude death and restoration in networks of oscillators with random-walk diffusion
• Pattern reconstruction through generalized eigenvectors on defective networks
• Modern Perspectives on Near-Equilibrium Analysis of Turing Systems