Projects per year
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 language | English |
---|---|
Article number | 5:12927 |
Pages (from-to) | 1 |
Number of pages | 10 |
Journal | Scientific Reports |
Volume | 5 |
Issue number | 12927 |
DOIs | |
Publication status | Published - 6 Aug 2015 |
Keywords
- complex networks
- turing patterns
- non linear dynamics
- cartesian product networks
- reaction-diffusion
- spatio-temporal patterns
Fingerprint
Dive into the research topics of 'Turing instabilities on Cartesian product networks'. Together they form a unique fingerprint.-
-
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
Activities
-
Control of self-organized patterns in complex networks
Timoteo Carletti (Speaker)
18 Jul 2017Activity: Participating in or organising an event types › Participation in workshop, seminar, course
-
Control of self-organized patterns in complex networks
Timoteo Carletti (Organiser)
18 Jul 2017Activity: Participating in or organising an event types › Participation in workshop, seminar, course
-
IAP VIII / 19 DYSCO - Dynamical SYStems Control and Optimization DYSCO Study day
Timoteo Carletti (Speaker)
1 Dec 2016Activity: Participating in or organising an event types › Participation to a Symposium, a study Day