@misc{Dierkes,
author = {Dierkes, Thomas},
title = {Construction of ODE systems from time series data by a highly flexible modelling approach},
issn = {1438-0064},
url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-56768},
abstract = {In this paper, a down-to-earth approach to purely data-based modelling of unknown dynamical systems is presented. Starting from a classical, explicit ODE formulation y=f(t,y) of a dynamical system, a method determining the unknown right-hand side f(t,y) from some trajectory data y_k(t_j), possibly very sparse, is given. As illustrative examples, a semi-standard predator-prey model is reconstructed from a data set describing the population numbers of hares and lynxes over a period of twenty years [1], and a simple damped pendulum system with a highly non-linear right-hand side is recovered from some artificial but very sparse data [2].},
language = {en}
}
@misc{VegaSchuetteConrad,
author = {Vega, Iliusi and Sch{\"u}tte, Christof and Conrad, Tim},
title = {SAIMeR: Self-adapted method for the identification of metastable states in real-world time series},
issn = {1438-0064},
url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-50130},
abstract = {In the framework of time series analysis with recurrence networks, we introduce SAIMeR, a heuristic self-adapted method that determines the elusive recurrence threshold and identifies metastable states in complex time series. To identify metastable states as well as the transitions between them, we use graph theory concepts and a fuzzy partitioning clustering algorithm. We illustrate SAIMeR by applying it to three real-world time series and show that it is able to identify metastable states in real-world data with noise and missing data points. Finally, we suggest a way to choose the embedding parameters used to construct the state space in which this method is performed, based on the analysis of how the values of these parameters affect two recurrence quantitative measurements: recurrence rate and entropy.},
language = {en}
}