Eur. Phys. J. B 58, 469-474 (2007)
https://doi.org/10.1140/epjb/e2007-00248-6

Mapping dynamical systems onto complex networks

¹ Escola Politécnica, Universidade Federal da Bahia, 40210-630 Salvador, Brazil
² Departamento de Economia, Universidade Católica de Brasília, 70790-160 Brasília, Brazil
³ Instituto de Física, Universidade Federal da Bahia, 40210-340 Salvador, Brazil

Corresponding authors: ^a ernesto@ufba.br - ^b danoc@pos.ucb.br - ^c randrade@ufba.br

Received: 30 October 2006
Revised: 30 July 2007
Published online: 22 September 2007

Abstract

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