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Reconstructing of equations of motion from time signals of nonlinear oscillators

  • Ohle, F.
  • Heck, C.W.
  • Max-Planck-Institut fuer Stroemungsforsc...
Publication Date
Jan 01, 1995
OpenGrey Repository


Stable modeling procedures are very important tools in modern nonlinear dynamics research. In this work a noval method is presented to reconstruct optimal low-dimensional models from experimental data of oscillatory systems. The main advantage of the introduced local-flow-method (LFM) compared to related modeling procedures such as the global-flow-method (GFM) of Cremers and Huebler is that a global model equation is reconstructed from the flow field but no information about the time evolution of the trajectory is needed, i.e., the time is not considered explicitly. This method allows the derivation of an adequate model, even if no transient data to the asymptotic solution are available or the reconstructed state space is not homogeneously filled with data. The applicability of the method will be discussed for a variety of nonlinear oscillators. It will be shown that even if most of the physical variables are hidden, the underlying low-dimensional model can be derived. Finally the notion of an optimal model, which is a measure of the qualitative and quantitative criteria of the reconstructed equation of motion will be discussed in detail. (orig.) / 46 refs. / Available from TIB Hannover: RA 1396(1995,8) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische Informationsbibliothek / SIGLE / DE / Germany

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