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DY: Fachverband Dynamik und Statistische Physik
DY 10: Posters I
DY 10.37: Poster
Monday, March 14, 2011, 17:00–19:00, P4
Continuous path-based measures for ε-recurrence networks — •Jonathan F. Donges1,2, Jobst Heitzig1, Reik V. Donner1, and Jürgen Kurths1,2 — 1Potsdam Institute for Climate Impact Research, P.O.Box 60 12 03, 14412 Potsdam, Germany — 2Department of Physics, Humboldt University of Berlin, Newtonstr. 15, 12489 Berlin, Germany
Continuous versions of various path-based graph-theoretical measures are defined for ε-recurrence networks, which have recently been successfully used in various applications of dynamical systems theory and time series analysis. We derive closed form expressions for two well-known one-dimensional maps as well as for the hypersphere and hypercube in various dimensions m. The latter problems are found to be closely linked to current research in probabilistic geometry and applied mathematics. Some comparison of the rigorous results to numerical estimates from ε-recurrence networks of finite length time series is also made. We argue that the proposed theory of path-based ε-recurrence network measures contributes substantially to a deeper understanding of the method of ε-recurrence network based time series analysis, which has already been utilized successfully in several distinct applications. Some geometrical applications of these measures, e.g., to define well-behaved measures of the convexity of a set, are also suggested.