Tune the topology to create or destroy patterns

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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 modication 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.
Original languageEnglish
PublisherNamur center for complex systems
Number of pages11
Publication statusPublished - 26 Apr 2016

Fingerprint

topology
embedding
emerging
broken symmetry
perturbation

Keywords

  • multigraph
  • spatio-temporal patterns
  • Complex Networks
  • Turing patterns
  • control

Cite this

Asllani, M., Carletti, T., & Fanelli, D. (2016). Tune the topology to create or destroy patterns. Namur center for complex systems.
Asllani, Malbor ; Carletti, Timoteo ; Fanelli, Duccio. / Tune the topology to create or destroy patterns. Namur center for complex systems, 2016. 11 p.
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author = "Malbor Asllani and Timoteo Carletti and Duccio Fanelli",
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Asllani, M, Carletti, T & Fanelli, D 2016, Tune the topology to create or destroy patterns. Namur center for complex systems.

Tune the topology to create or destroy patterns. / Asllani, Malbor; Carletti, Timoteo; Fanelli, Duccio.

Namur center for complex systems, 2016. 11 p.

Research output: Book/Report/JournalOther report

TY - BOOK

T1 - Tune the topology to create or destroy patterns

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N2 - 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 modication 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.

AB - 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 modication 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.

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KW - spatio-temporal patterns

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KW - control

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Asllani M, Carletti T, Fanelli D. Tune the topology to create or destroy patterns. Namur center for complex systems, 2016. 11 p.