Mapping dynamical systems onto complex networks

Details Mapping dynamical systems onto complex networks Mapping dynamical systems onto complex networks

2006-10-30

arxiv.org/abs/cond-mat/0610820v2

Eur. Phys. J. B 58, 469-474 (2007)

Physics

Condensed Matter

Statistical Mechanics

13 pages, 8 eps files in 5 figures

Scientific paper

10.1140/epjb/e2007-00248-6

A procedure to characterize chaotic dynamical systems with concepts of complex networks is pursued, in which a dynamical system is mapped onto a network. The nodes represent the regions of space visited by the system, while edges represent the transitions between these regions. Parameters used to quantify the properties of complex networks, including those related to higher order neighborhoods, are used in the analysis. The methodology is tested for the logistic map, focusing the onset of chaos and chaotic regimes. It is found that the corresponding networks show distinct features, which are associated to the particular type of dynamics that have generated them.

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