Entropy of weighted recurrence plots.
The Shannon entropy of a time series is a standard measure to assess the complexity of a dynamical process and can be used to quantify transitions between different dynamical regimes. An alternative way of quantifying complexity is based on state recurrences, such as those available in recurrence quantification analysis. Although varying definitions for recurrence-based entropies have been suggested so far, for some cases they reveal inconsistent results. Here we suggest a method based on weighted recurrence plots and show that the associated Shannon entropy is positively correlated with the largest Lyapunov exponent. We demonstrate the potential on a prototypical example as well as on experimental data of a chemical experiment.
Potsdam Institute for Climate Impact Research, 14473 Potsdam, Germany and Department of Physics, Humboldt University, 12489 Berlin, Germany.
Deniz
D
Eroglu
Instituto de Física de São Carlos, Universidade de São Paulo, 13566-590 São Carlos, São Paulo, Brazil.
Thomas K Dm
TK
Peron
Potsdam Institute for Climate Impact Research, 14473 Potsdam, Germany.
Nobert
N
Marwan
Departamento de Matemática Aplicada e Estatística, Instituto de Ciências Matemáticas e de Computação,Universidade de São Paulo, Caixa Postal 668,13560-970 São Carlos, São Paulo, Brazil.
Francisco A
FA
Rodrigues
Instituto de Física de São Carlos, Universidade de São Paulo, 13566-590 São Carlos, São Paulo, Brazil.
Luciano da F
Lda F
Costa
Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St. Louis, Missouri 63103, USA.
Michael
M
Sebek
Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St. Louis, Missouri 63103, USA.
István Z
IZ
Kiss
Potsdam Institute for Climate Impact Research, 14473 Potsdam, Germany and Department of Physics, Humboldt University, 12489 Berlin, Germany and Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom.
Jürgen
J
Kurths