5676
eng
reportzib
0
--
2015-12-11
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Construction of ODE systems from time series data by a highly flexible modelling approach
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].
1438-0064
urn:nbn:de:0297-zib-56768
Published in ArXiv
no
Thomas Dierkes
Mascha Berg
ZIB-Report
15-59
Time series analysis
Inverse problems
Systems biology, networks
Population dynamics (general)
Numerical Mathematics
Computational Systems Biology
Dierkes, Thomas
GynSys
P4milk
PAEON
https://opus4.kobv.de/opus4-zib/files/5676/ZIBReport_GenericYetFlexible.pdf
5013
eng
reportzib
0
--
2014-05-16
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SAIMeR: Self-adapted method for the identification of metastable states in real-world time series
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.
1438-0064
urn:nbn:de:0297-zib-50130
Iliusi Vega
Erlinda Körnig
Christof Schütte
Tim Conrad
ZIB-Report
14-16
eng
uncontrolled
time series analysis
eng
uncontrolled
application in statistical physics
eng
uncontrolled
recurrence quantification analysis
eng
uncontrolled
threshold
eng
uncontrolled
metastability
eng
uncontrolled
non-linear dynamics
Time series analysis
Applications in statistical physics
Classification and discrimination; cluster analysis [See also 68T10]
Numerical Mathematics
Visual Data Analysis
Schütte, Christof
Conrad, Tim
Bioinformatics in Medicine
https://opus4.kobv.de/opus4-zib/files/5013/ZIB-Report_14-16.pdf