title: Using waveform information in nonlinear data assimilation.
abstract: Information in measurements of a nonlinear dynamical system can be transferred to a quantitative model of the observed system to establish its fixed parameters and unobserved state variables. After this learning period is complete, one may predict the model response to new forces and, when successful, these predictions will match additional observations. This adjustment process encounters problems when the model is nonlinear and chaotic because dynamical instability impedes the transfer of information from the data to the model when the number of measurements at each observation time is insufficient. We discuss the use of information in the waveform of the data, realized through a time delayed collection of measurements, to provide additional stability and accuracy to this search procedure. Several examples are explored, including a few familiar nonlinear dynamical systems and small networks of Colpitts oscillators.
authors.affiliation: Department of Physics, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0374, USA.
authors.forename: Daniel
authors.initials: D
authors.lastname: Rey
authors.affiliation: Department of Physics, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0374, USA.
authors.forename: Michael
authors.initials: M
authors.lastname: Eldridge
authors.affiliation: Department of Physics, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0374, USA.
authors.forename: Uriel
authors.initials: U
authors.lastname: Morone
authors.affiliation: Department of Physics, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0374, USA.
authors.forename: Henry D I
authors.initials: HD
authors.lastname: Abarbanel
authors.affiliation: Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany and Institute for Nonlinear Dynamics, Georg-August-Universität Göttingen, Am Fassberg 17, 37077 Göttingen, Germany.
authors.forename: Ulrich
authors.initials: U
authors.lastname: Parlitz
authors.affiliation: Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany and Institute for Nonlinear Dynamics, Georg-August-Universität Göttingen, Am Fassberg 17, 37077 Göttingen, Germany.
authors.forename: Jan
authors.initials: J
authors.lastname: Schumann-Bischoff