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Article overview
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Crafting networks to achieve (or not) chaotic states | Sarah De Nigris
; Xavier Leoncini
; | Date: |
15 Sep 2014 | Abstract: | The influence of networks topology on collective properties of dynamical
systems defined upon it is studied in the thermodynamic limit. A network model
construction scheme is proposed where the number of links, the average
eccentricity and the clustering coefficient are controlled. This is done by
rewiring links of a regular one dimensional chain according to a probability
$p$ within a specific range $r$, that can depend on the number of vertices $N$.
We compute the thermodynamic behavior of a system defined on the network, the
$XY-$rotors model, and monitor how it is affected by the topological changes.
We identify the network dimension $d$ as a crucial parameter: topologies with
$d<2$ exhibit no phase transitions while ones with $d>2$ display a second order
phase transition. Topologies with $d=2$ exhibit states characterized by
infinite susceptibility and macroscopic chaotic/turbulent dynamical behavior.
These features are also captured by $d$ in the finite size context. | Source: | arXiv, 1409.5016 | Services: | Forum | Review | PDF | Favorites |
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