Construction and analysis of differential equations from experimental time series of oscillatory systems

DOI10.1016/0167-2789(92)90178-PzbMath0754.34034OpenAlexW2078018827MaRDI QIDQ1197528

Helmut Eckelmann, Frank Ohle, Bernd R. Noack

Publication date: 16 January 1993

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(92)90178-p

zbMATH Keywords

evolution equationHopf bifurcationFloquet theoryvelocity fluctuationLandau equationtransient behaviourexperimental time seriesautonomous system of ordinary differential equationsvan der Pol transformationconstructing a differential equation from an experimental time signallaminar periodic wake behind a circular cylinderlimit-cycle dynamicsperiodic-doubling cascade

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Bifurcation theory for ordinary differential equations (34C23) Navier-Stokes equations (35Q30) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Inverse problems involving ordinary differential equations (34A55) Wakes and jets (76D25)

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Discrete-time dynamical systems under observational uncertainty ⋮ Reconstruction of blurred orbits under finite resolution

Cites Work

• Optimal shadowing and noise reduction
• Extracting qualitative dynamics from experimental data
• Note concerning our paper On the nature of turbulence. Commun. math. Phys. 20, 167-192 (1971)
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