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29 March 2024
 
  » arxiv » 1409.5016

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Crafting networks to achieve (or not) chaotic states
Sarah De Nigris ; Xavier Leoncini ;
Date 15 Sep 2014
AbstractThe 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
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