Tune the topology to create or destroy patterns
@article{Asllani2016TuneTT, title={Tune the topology to create or destroy patterns}, author={Malbor Asllani and Timot{\'e}o Carletti and Duccio Fanelli}, journal={The European Physical Journal B}, year={2016}, volume={89}, pages={1-10} }
Abstract
We consider the dynamics of a reaction-diffusion system on a multigraph. The species
share the same set of nodes but can access different links to explore the embedding
spatial support. By acting on the topology of the networks we can control the ability of
the system to self-organise in macroscopic patterns, emerging as a symmetry breaking
instability of an homogeneous fixed point. Two different cases study are considered: on
the one side, we produce a global modification of the…
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References
SHOWING 1-10 OF 38 REFERENCES
The theory of pattern formation on directed networks.
- MathematicsNature communications
- 2014
The theory of pattern formation in reaction-diffusion systems defined on symmetric networks is extended to the case of directed networks, which are found in a number of different fields, such as neuroscience, computer networks and traffic systems.
Turing patterns in multiplex networks.
- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2014
The theory of patterns formation for a reaction-diffusion system defined on a multiplex is developed by means of a perturbative approach. The interlayer diffusion constants act as a small parameter…
The physics of spreading processes in multilayer networks
- Computer Science
- 2016
Progress is surveyed towards attaining a deeper understanding of spreading processes on multilayer networks, and some of the physical phenomena related to spreading processes that emerge from multilayered structure are highlighted.
Collective dynamics of ‘small-world’ networks
- Computer ScienceNature
- 1998
Simple models of networks that can be tuned through this middle ground: regular networks ‘rewired’ to introduce increasing amounts of disorder are explored, finding that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs.
Pattern formation in multiplex networks
- Computer ScienceScientific reports
- 2015
The theory demonstrates that the existence of such topology-driven instabilities is generic in multiplex networks, providing a new mechanism of pattern formation.
Renormalization Group Analysis of the Small-World Network Model
- Physics, Computer Science
- 1999
Approximating spectral impact of structural perturbations in large networks.
- Mathematics, Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2010
A theory for estimating the change of the largest eigenvalue of the adjacency matrix or the extreme eigenvalues of the graph Laplacian when small but arbitrary set of links are added or removed from the network is developed.
Controllability of complex networks
- Computer ScienceNature
- 2011
Analytical tools are developed to study the controllability of an arbitrary complex directed network, identifying the set of driver nodes with time-dependent control that can guide the system’s entire dynamics.
Localized Patterns in Reaction-Diffusion Systems
- Mathematics
- 1980
A new chemical pattern is discussed, which is a propagationless solitary island in an infinite medium. We demonstrate analytically its existence and stability for a certain simple model. The…
Laplacian spectra as a diagnostic tool for network structure and dynamics.
- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2008
The effects of clustering, degree distribution, and a particular type of coupling asymmetry (input normalization), all of which are known to have effects on the synchronizability of oscillator networks, are studied.