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Turing instabilities on Cartesian product networks

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 Laplaci...

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Autores principales: Asllani, Malbor, Busiello, Daniel M., Carletti, Timoteo, Fanelli, Duccio, Planchon, Gwendoline
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group 2015
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4526855/
https://www.ncbi.nlm.nih.gov/pubmed/26245138
http://dx.doi.org/10.1038/srep12927
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author Asllani, Malbor
Busiello, Daniel M.
Carletti, Timoteo
Fanelli, Duccio
Planchon, Gwendoline
author_facet Asllani, Malbor
Busiello, Daniel M.
Carletti, Timoteo
Fanelli, Duccio
Planchon, Gwendoline
author_sort Asllani, Malbor
collection PubMed
description 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.
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spelling pubmed-45268552015-08-07 Turing instabilities on Cartesian product networks Asllani, Malbor Busiello, Daniel M. Carletti, Timoteo Fanelli, Duccio Planchon, Gwendoline Sci Rep Article 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. Nature Publishing Group 2015-08-06 /pmc/articles/PMC4526855/ /pubmed/26245138 http://dx.doi.org/10.1038/srep12927 Text en Copyright © 2015, Macmillan Publishers Limited http://creativecommons.org/licenses/by/4.0/ This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/
spellingShingle Article
Asllani, Malbor
Busiello, Daniel M.
Carletti, Timoteo
Fanelli, Duccio
Planchon, Gwendoline
Turing instabilities on Cartesian product networks
title Turing instabilities on Cartesian product networks
title_full Turing instabilities on Cartesian product networks
title_fullStr Turing instabilities on Cartesian product networks
title_full_unstemmed Turing instabilities on Cartesian product networks
title_short Turing instabilities on Cartesian product networks
title_sort turing instabilities on cartesian product networks
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4526855/
https://www.ncbi.nlm.nih.gov/pubmed/26245138
http://dx.doi.org/10.1038/srep12927
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