Tune the topology to create or destroy patterns

Research output: Contribution to journalArticle

Abstract

We consider the dynamics of a reaction-diffusion system on a multigraph. The speciesshare the same set of nodes but can access different links to explore the embeddingspatial support. By acting on the topology of the networks we can control the ability ofthe system to self-organise in macroscopic patterns, emerging as a symmetry breakinginstability of an homogeneous fixed point. Two different cases study are considered: onthe one side, we produce a global modification of the networks, starting from the limitingsetting where species are hosted on the same graph. On the other, we consider the effectof inserting just one additional single link to differentiate the two graphs. In bothcases, patterns can be generated or destroyed, as follows the imposed, small, topologicalperturbation. Approximate analytical formulae allow to grasp the essence of the phenomenonand can potentially inspire innovative control strategies to shape the macroscopicdynamics on multigraph networks.

Original languageEnglish
Article number260
JournalEuropean Physical Journal B
Volume89
Issue number12
DOIs
Publication statusPublished - 1 Dec 2016

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topology
Topology
emerging
symmetry

Keywords

  • turing patterns
  • complex networks
  • reaction diffusion
  • control
  • multigraph

Cite this

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title = "Tune the topology to create or destroy patterns",
abstract = "We consider the dynamics of a reaction-diffusion system on a multigraph. The speciesshare the same set of nodes but can access different links to explore the embeddingspatial support. By acting on the topology of the networks we can control the ability ofthe system to self-organise in macroscopic patterns, emerging as a symmetry breakinginstability of an homogeneous fixed point. Two different cases study are considered: onthe one side, we produce a global modification of the networks, starting from the limitingsetting where species are hosted on the same graph. On the other, we consider the effectof inserting just one additional single link to differentiate the two graphs. In bothcases, patterns can be generated or destroyed, as follows the imposed, small, topologicalperturbation. Approximate analytical formulae allow to grasp the essence of the phenomenonand can potentially inspire innovative control strategies to shape the macroscopicdynamics on multigraph networks.",
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Tune the topology to create or destroy patterns. / Asllani, Malbor; Carletti, Timoteo; Fanelli, Duccio.

In: European Physical Journal B, Vol. 89, No. 12, 260, 01.12.2016.

Research output: Contribution to journalArticle

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AU - Carletti, Timoteo

AU - Fanelli, Duccio

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