@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} }