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Tune the topology to create or destroy patterns

Author

Listed:
  • Malbor Asllani

    (naXys, Namur Center for Complex Systems, University of Namur)

  • Timoteo Carletti

    (naXys, Namur Center for Complex Systems, University of Namur)

  • Duccio Fanelli

    (Dipartimento di Fisica e Astronomia, University of Florence)

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.

Suggested Citation

  • Malbor Asllani & Timoteo Carletti & Duccio Fanelli, 2016. "Tune the topology to create or destroy patterns," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 89(12), pages 1-10, December.
    • Handle: RePEc:spr:eurphb:v:89:y:2016:i:12:d:10.1140_epjb_e2016-70248-6
    DOI: 10.1140/epjb/e2016-70248-6
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    Cited by:

    1. Muolo, Riccardo & Carletti, Timoteo & Bianconi, Ginestra, 2024. "The three way Dirac operator and dynamical Turing and Dirac induced patterns on nodes and links," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).

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    Keywords

    Statistical and Nonlinear Physics;

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