title: Optimized spectral estimation for nonlinear synchronizing systems.
abstract: In many fields of research nonlinear dynamical systems are investigated. When more than one process is measured, besides the distinct properties of the individual processes, their interactions are of interest. Often linear methods such as coherence are used for the analysis. The estimation of coherence can lead to false conclusions when applied without fulfilling several key assumptions. We introduce a data driven method to optimize the choice of the parameters for spectral estimation. Its applicability is demonstrated based on analytical calculations and exemplified in a simulation study. We complete our investigation with an application to nonlinear tremor signals in Parkinson's disease. In particular, we analyze electroencephalogram and electromyogram data.
authors.affiliation: Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom and Department of Physics, University of Freiburg, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany and Freiburg Center for Data Analysis and Modeling (FDM), University of Freiburg, Eckerstrasse 1, 79104 Freiburg, Germany and Freiburg Institute for Advanced Studies (FRIAS), University of Freiburg, Albertstrasse 19, 79104 Freiburg, Germany.
authors.forename: Linda
authors.initials: L
authors.lastname: Sommerlade
authors.affiliation: Department of Physics, University of Freiburg, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany and Freiburg Center for Data Analysis and Modeling (FDM), University of Freiburg, Eckerstrasse 1, 79104 Freiburg, Germany and Hospital for Neuropaediatrics and Muscular Diseases, University Medical Center of Freiburg, Germany.
authors.forename: Malenka
authors.initials: M
authors.lastname: Mader
authors.affiliation: Department of Physics, University of Freiburg, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany and Freiburg Center for Data Analysis and Modeling (FDM), University of Freiburg, Eckerstrasse 1, 79104 Freiburg, Germany.
authors.forename: Wolfgang
authors.initials: W
authors.lastname: Mader
authors.affiliation: Department of Physics, University of Freiburg, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany and Freiburg Center for Data Analysis and Modeling (FDM), University of Freiburg, Eckerstrasse 1, 79104 Freiburg, Germany and Freiburg Institute for Advanced Studies (FRIAS), University of Freiburg, Albertstrasse 19, 79104 Freiburg, Germany.
authors.forename: Jens
authors.initials: J
authors.lastname: Timmer
authors.affiliation: Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom.
authors.forename: Marco
authors.initials: M
authors.lastname: Thiel
authors.affiliation: Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom and Freiburg Institute for Advanced Studies (FRIAS), University of Freiburg, Albertstrasse 19, 79104 Freiburg, Germany.
authors.forename: Celso
authors.initials: C
authors.lastname: Grebogi
authors.affiliation: Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom and Freiburg Center for Data Analysis and Modeling (FDM), University of Freiburg, Eckerstrasse 1, 79104 Freiburg, Germany.
authors.forename: Björn
authors.initials: B
authors.lastname: Schelter
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D004569:Electroencephalography / Q000379:methods*; D004576:Electromyography / Q000379:methods*; D006801:Humans; D008954:Models, Biological; D017711:Nonlinear Dynamics; D010300:Parkinson Disease / Q000150:complications / Q000503:physiopathology*; D014202:Tremor / Q000209:etiology / Q000503:physiopathology*