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Article overview
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Multiple scale theory of topology driven pattern on directed networks | Silvia Contemori
; Francesca Di Patti
; Duccio Fanelli
; Filippo Miele
; | Date: |
1 Aug 2015 | Abstract: | Dynamical processes on networks are currently being considered in different
domains of cross-disciplinary interest. Reaction-diffusion systems hosted on
directed graphs are in particular relevant for their widespread applications,
from neuroscience, to computer networks and traffic systems. Due to the
peculiar spectrum of the discrete Laplacian operator, homogeneous fixed points
can turn unstable, on a directed support, because of the topology of the
network, a phenomenon which cannot be induced on undirected graphs. A linear
analysis can be performed to single out the conditions that underly the
instability. The complete characterization of the patterns, which are
eventually attained beyond the linear regime of exponential growth, calls
instead for a full non linear treatment. By performing a multiple time scale
perturbative calculation, we here derive an effective equation for the non
linear evolution of the amplitude of the most unstable mode, close to the
threshold of criticality. This is a Stuart-Landau equation whose complex
coefficients appear to depend on the topological features of the embedding
directed graph. The theory proves adequate versus simulations, as confirmed by
operating with a paradigmatic reaction-diffusion model. | Source: | arXiv, 1508.0148 | Services: | Forum | Review | PDF | Favorites |
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