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Abstract
The problem of Turing instabilities for a reactiondiffusion 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 subgraphs. 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 MimuraMurray reaction kinetics confirm the adequacy of the proposed theory.
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 subgraphs. 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 MimuraMurray reaction kinetics confirm the adequacy of the proposed theory.
Original language  English 

Publisher  Namur center for complex systems 
Number of pages  10 
Volume  13 
Edition  14 
Publication status  Published  1 Dec 2014 
Publication series
Name  naXys Technical Report Series 

Publisher  University of Namur 
No.  14 
Volume  13 
Keywords
 complex networks
 turing patterns
 non linear dynamics
 cartesian product networks
 reactiondiffusion
 spatiotemporal patterns
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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.
1/04/12 → 30/09/17
Project: Research