Turing instabilities on Cartesian product networks

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

Research output: Contribution to journalArticle

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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

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Turing Instability
Cartesian product
Discrete Laplacian
Discrete Operators
Reaction Kinetics
Dispersion Relation
Reaction-diffusion System
Cartesian
Tensor Product
Eigenvector
Expand
Explicit Formula
Subgraph
Wavelength
Eigenvalue
Perturbation
Numerical Simulation

Keywords

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

Cite this

Asllani, Malbor ; Busiello, Daniel M. ; Carletti, Timoteo ; Fanelli, Duccio ; Planchon, Gwendoline. / Turing instabilities on Cartesian product networks. In: Scientific Reports. 2015 ; Vol. 5, No. 12927. pp. 1.
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Asllani, M, Busiello, DM, Carletti, T, Fanelli, D & Planchon, G 2015, 'Turing instabilities on Cartesian product networks', Scientific Reports, vol. 5, no. 12927, 5:12927, pp. 1. https://doi.org/doi:10.1038/srep12927

Turing instabilities on Cartesian product networks. / Asllani, Malbor; Busiello, Daniel M.; Carletti, Timoteo; Fanelli, Duccio; Planchon, Gwendoline.

In: Scientific Reports, Vol. 5, No. 12927, 5:12927, 06.08.2015, p. 1.

Research output: Contribution to journalArticle

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