Turing instabilities on Cartesian product networks

Malbor Asllani, Daniel M. Busiello, Timoteo Carletti, Duccio Fanelli, Gwendoline Planchon

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Abstract

The problem of Turing instabilities for a reaction-diffusion system defined on a complex Cartesian product network is considered. To this end we operate in the linear regime and expand the time dependent perturbation on a basis formed by the tensor product of the eigenvectors of the discrete Laplacian operators, associated to each of the individual networks that build the Cartesian product. The dispersion relation which controls the onset of the instability depends on a set of discrete wavelengths, the eigenvalues of the aforementioned Laplacians. Patterns can develop on the Cartesian network, if they are supported on at least one of its constitutive sub-graphs. Multiplex networks are also obtained under specific prescriptions. In this case, the criteria for the instability reduce to compact explicit formulae. Numerical simulations carried out for the Mimura-Murray reaction kinetics confirm the adequacy of the proposed theory.
Original languageEnglish
Article number5:12927
Pages (from-to)1
Number of pages10
JournalScientific Reports
Volume5
Issue number12927
DOIs
Publication statusPublished - 6 Aug 2015

Keywords

  • complex networks
  • turing patterns
  • non linear dynamics
  • cartesian product networks
  • reaction-diffusion
  • spatio-temporal patterns

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  • Projects

    PAI n°P7/19 - DYSCO: Dynamical systems, control and optimization (DYSCO)

    WINKIN, J., Blondel, V., Vandewalle, J., Pintelon, R., Sepulchre, R., Vande Wouwer, A. & SARTENAER, A.

    1/04/1230/09/17

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    Activities

    • 4 Participation in workshop, seminar, course
    • 3 Participation in conference
    • 1 Participation to a Symposium, a study Day

    Control of self-organized patterns in complex networks

    Timoteo Carletti (Organiser)

    18 Jul 2017

    Activity: Participating in or organising an event typesParticipation in workshop, seminar, course

    Control of self-organized patterns in complex networks

    Timoteo Carletti (Speaker)

    18 Jul 2017

    Activity: Participating in or organising an event typesParticipation in workshop, seminar, course

    IAP VIII / 19 DYSCO - Dynamical SYStems Control and Optimization DYSCO Study day

    Timoteo Carletti (Speaker)

    1 Dec 2016

    Activity: Participating in or organising an event typesParticipation to a Symposium, a study Day

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