ECONS - WGL PAKT Initiative - Evolving Complex Networks
Regional resource management under environmental and demographic change

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International Journal of Bifurcation and Chaos, 21(4), 1019–1046 (2011) DOI:10.1142/S0218127411029021

Recurrence-based time series analysis by means of complex network methods

R. V. Donner, M. Small, J. F. Donges, N. Marwan, Y. Zou, R. Xiang, J. Kurths

Complex networks are an important paradigm of modern complex systems sciences which allows quantitatively assessing the structural properties of systems composed of different interacting entities. During the last years, intensive efforts have been spent on applying network-based concepts also for the analysis of dynamically relevant higher-order statistical properties of time series. Notably, many corresponding approaches are closely related with the concept of recurrence in phase space. In this paper, we review recent methodological advances in time series analysis based on complex networks, with a special emphasis on methods founded on recurrence plots. The potentials and limitations of the individual methods are discussed and illustrated for paradigmatic examples of dynamical systems as well as for real-world time series. Complex network measures are shown to provide complementary information about structural features of dynamical systems that substantially enrich the knowledge gathered from other existing (linear as well as nonlinear) methods.