Publications with Abstracts by Alfred Hübler (1991)

1. * R. Wittmann, A. Hübler, E. Lüscher, An Experiment for the Examination of Dendritic River Systems, Naturwissenschaften 78, 23 (1991)

2. * T. Eisenhammer, A. Hübler. N. Packard, J.C.S. Kelso, Modeling Experimental Time Series with Ordinary Differential Equations, Biol. Cybern 65, 107-112 (1991)
   Abstract: Recently some methods have been presented to extract ordinary differential equations (ODE) directly from en experimental time series. Here, we introduce a new method to find an ODE which models both the short time and the long time dynamics. The experimental data are represented in a state space and the corresponding flow vector are approximated by polynomials of the state vector components. We apply these methods both to simulated data and experimental data from human limb movements, which like many other biological systems can exhibit limit cycle dynamics. In systems with only one oscillator there is excellent agreement between the limit cycling displayed by the experimental system and the reconstructed model, even if the data are very noisy. Furthermore, we study systems of who coupled limit cycle oscillators. There, a reconstruction was only successful for data with a sufficiently long transient trajectory and relatively low noise level.

   Reprint

3. * R. Shermer, A. Hübler, N.H.Packard, Model-based Control of the Burgers Equation, Phys.Rev. A 43, 5642-5654 (1991)
   Abstract: We extend a method of control, model-based control, to the realm of partial differential equations. The hallmark of model-based control is that a particular goal dynamics is achieved by using a model for the observed dynamics to create the appropriate driving needed to make the goal dynamics an attractor for the system, alleviating the need for constant feedback, as is necessary with traditional control methods. We investigate a model-based control for the Burgers equation, with particular attention to sensitivity of the control to model inaccuracies, boundary errors, and noise.

   Reprint

4. * K. Chang, A. Kodogeorgiou, A. Hübler, E.A. Jackson, General Resonance Spectroscopy, Physics D 51, 99-108 (1991)
   Abstract: We introduce a generalized definition of resonance which is applicable to systems without well-defined energies and derive an approximate expression for the shape of the resonance curves. We also provide an algorithm for modeling the dynamics of an experimental system using this generalized resonance function.

   Reprint

5. E. Roesch, F. Ohle, H. Eckelmann, A. Hübler, Modeling and Control of Karman Vortex Streets, in The Global Geometry of Turbulence, J. Jimenez (ed.), Plenum Press, NY (1991)

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