Construction of ODE systems from time series data by a highly flexible modelling approach

Please always quote using this URN: urn:nbn:de:0297-zib-56768
  • 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].

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Author:Thomas Dierkes
Document Type:ZIB-Report
MSC-Classification:37-XX DYNAMICAL SYSTEMS AND ERGODIC THEORY [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] / 37Mxx Approximation methods and numerical treatment of dynamical systems [See also 65Pxx] / 37M10 Time series analysis
65-XX NUMERICAL ANALYSIS / 65Lxx Ordinary differential equations / 65L09 Inverse problems
92-XX BIOLOGY AND OTHER NATURAL SCIENCES / 92Cxx Physiological, cellular and medical topics / 92C42 Systems biology, networks
92-XX BIOLOGY AND OTHER NATURAL SCIENCES / 92Dxx Genetics and population dynamics / 92D25 Population dynamics (general)
Date of first Publication:2015/12/11
Series (Serial Number):ZIB-Report (15-59)
ISSN:1438-0064
Published in:Published in ArXiv