Crafting networks to achieve, or not achieve, chaotic states

Sarah De Nigris, Xavier Leoncini

Research output: Contribution to journalArticlepeer-review

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 and the average eccentricity 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 thermodynamical 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 effective dimension d as a crucial parameter: topologies with d<2 exhibit no phase transitions, while topologies 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.

Original languageEnglish
Article number042809
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume91
Issue number4
DOIs
Publication statusPublished - 27 Apr 2015

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