Publications with Abstracts by Alfred Hübler (1989)

1. A. Hübler, Adaptive Control of Chaotic Systems, Helv.Phys.Acta 62, 343 (1989)
   Abstract: In order to describe the chaotic dynamics of a nonlinear system, a discrete map is reconstructed form the time series of an experimental system. The parameters of the map may depend on time. The map is a model for the dynamics of the experimental system. This model can be used in order to control the dynamics of the experimental system with small external perturbations, e.g. in order to get a special periodic dynamics or a special type of chaos. We argue that modeling and controlling can be done simultaneously.

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2. A. Hübler, R. Georgii, W. Eberl. E. Lüscher, Resonant Stimulation and Control of Nonlinear Mechanical Pendulum by Poincare Maps, Helv.Phys.Acta 62, 290-293 (1989)
   Abstract: A new method for resonant stimulation of nonlinear damped oscillators by nonlinear entrainment is presented. Appropriate driving forces are calculated with Poincare maps. These maps can be extracted from experimental time series. We show experimentally, that the resonant driving forces are in phase with the velocity of the oscillator and cause a huge energy transfer. The corresponding driving forces are aperiodic and can be calculated without any feed back from the experiment.

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3. M. Rose, T. Kautzky, P. Deisz, A. Hübler. E. Lüscher, Resonant Stimulation and Control of Karman's Vortex Street, Helv.Phys.Acta 62, 286-289 (1989)
   Abstract: We show that the periodic dynamics of a vortex street behind a circular cylinder can be modeled by a low dimensional system of ordinary differential equations with a few parameters, although the system has infinitely many degrees of freedom. The parameters depend on the hydrodynamic control parameters. We show experimentally that the dynamics is mainly on an inertial manifold. All degrees of freedom destinating away from the inertial manifold are slaved. Furthermore we shoe, that the system can be controlled by sinusoidal acoustic perturbations. The system remains on the inertial manifold if the perturbations are resonant.

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4. F. Dinkelacker, P.Deisz, A. Hübler, E, Lüscher, Properties of Hydrodynamic Systems with Flexible Boundary Conditions, Helv.Phys.Acta 62, 282-285 (1989)
   Abstract: In a circular channel we investigate experimentally the dynamics of a solid body which can move perpendicular to the axis of the channel. If the flow in the tube is slow and steady the stable stationary state of the system satisfies a variational principle. We show that this state the Reynolds number reaches its maximum value. A generalization of these results for bodies with deformable boundary conditions might have important applications in technical hydrodynamics.

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5. M. Athelogou, B. Merte, P. Deisz, A. Hübler, E, Lüscher, Extremal Properties of Dendritic Patterns: Biophysical Applications I, Helv.Phys.Acta 62, 250 (1989)
   Abstract: Recent experiments indicate that stable agglomerations of metallic balls in an electric field can have a fractal geometry and a dendritic structure. Further it has been shown, that these patterns satisfy a variational principle. We compare the geometry of these optimal patterns with dendritic structures of biological systems, e.g. the nervous system, roots. We discuss the relationship between the variational principle and the function of these roots.

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   M. Athelogou, B. Merte, P. Deisz, A. Hübler, E. Lüscher, Extremal Properties of Dentritic Patterns: Biophysical Applications II, Helv.Phys.Acta 62, 908 (1989)

   Abstract: Stationary dendritic patterns, as e.g. stable agglomerates of metallic spheres in an electric field, exhibit extremal properties. Biological systems, like root systems of plants, show dendritic structures. A biological potential for such biological systems is defined. Experiments show that this biological potential is minimal in the stationary state.

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6. E. Lüscher, A. Hübler, Resonant Stimulation of Complex Systems, Helv.Phys.Acta 62, 908 (1989)
   Abstract: The dynamics of a huge variety of complex systems can be estimated from a low dimensional system of ordinary differential equations, although the number of degrees of freedom is large. Nearly all variables are slaved by a few order parameters. If the complex system is perturbed by an external force, slaved variables can be stimulated and a prediction of the response from the low dimensional system of differential equations is impossible. We show that it is generally possible to predict the response of the complex system, and to control the complex system, if the external forces are resonant perturbations.

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7. A. Wandelt, W. Eberl, A. Hübler, E. Lüscher, Transformation to Normal Time for the Calculation of Poincare Maps in a Closed Form, Helv.Phys.Acta 62, 339 (1989)
   Abstract: The calculation of Poincare maps can be simplified by introducing a special rescaling of the flow vector field, namely the transformation to normal time. If that is done in an appropriate way, one can calculate the Poincare map analytically.

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8. B. Merte, G. Hadwich, B. Binias, P. Deisz, A. Hübler, E. Lüscher, Formation of Selfsimilar Dendritic Patterns with Extremal Properties, Helv.Phys.Acta 62, 293 (1989)
   Abstract: Under the influence of an electric current I small metallic balls from a stable, stationary dendritic pattern exhibiting extremal properties. The corresponding quantity as well as the fractal geometry are experimentally studied as a function of time and the control parameters of the system. The results are compared to those obtained for transient dendritic structures, e.g. electrodeposits.

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9. Ch. Scholz, M. Fuchs, W. Eberl, A. Hübler, E. Lüscher, Connection of Parallel Computers Using Navier-Stokes-Equation for Data Flow Optimization, to appear in Helv.Phys.Acta
   Abstract: The Navier-Stokes equation (NSE) can be derived from the principle of least action, that means liquid particles in a field are moving with least action. It will be examined, if – instead of liquid particles in a field of forces – data can stream in a field of computers. The resulting self-organization would have to be an optimal connection of data sources and sinks. The NSE can be solved numerically and globally or asynchronously and locally.

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10. H.C. Schulz, M. Rose, T. Kautzky, A. Hübler, E. Lüscher, Algorithms for the Construction of Differential Equations from Experimental Data, to appear in Helv.Phys.Acta
    Abstract: The dynamics of a Karman vortex street (KVS) in its periodic regime can be modeled by a low dimensional system of ordinary differential equations (ODE). It can be deduced from the state space representation of measured time series, that a suitable form of this ODE is an extended Van der Pol equation (1) To obtain the coefficients of the ODE, we present a new fit method, which is able to recognize typical dynamical features of the system, e.g. stability of limit cycles, even from data with high noise level and small transients.

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11. K. Chang, A. Hübler, N. Packard, Universal Properties of the Resonance Curve of Complex Systems, in "Quantitative Measures of Complex Dynamical Systems", N.B. Abraham (Ed.), Plenum Press, New York, 1989
    Abstract: The dynamics of a large variety of complex systems are confined to a low-dimensional manifold. We show that the resonance curve of those systems has universal shape. The parameters of the resonance curve can be used to characterize a complex system.

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12. * A. Hübler, E. Lüscher, Resonant Stimulation and Control of Nonlinear Oscillators, Naturwissenschaften 76, 67-69 (1989)

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13. G. Mayer-Kress, A. Hübler, Time Evolution of Local Complexity Measures and Aperiodic Perturbations of Nonlinear Dynamical Systems, in "Quantitative Measures of Complex Dynamical Systems", N.B. Abraham (Ed.), Plenum Press, New York, 1989
    Abstract: We discuss numerical algorithms for estimating dimensional complexity of observed time-series with special emphasis on biological and medical applications. Factors which enter the procedure are discussed and applied to local estimates of pointwise dimensions or crowding indices. We illustrate the concepts with the help of experimental time-series obtained from speech signals. The temporal evolution of the crowding index shoes oscillations which can be correlated with properties of the time-series. We compare the time evolution of the dimensional complexity parameter with the original time-series and also with recurrence plots of the embedded time series.

    Besides the analysis of spontaneous activity of biological systems it is often more useful to study event related potentials. We have generalizes our analysis code in a way that attractors can also be reconstructed from such non contiguous signals. Finally we discuss the possible applications of this method to habituation phenomena and diagnostic use in event-related potentials.

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14. D. Bensen, M. Welge, A. Hübler, N. Packard, Characterization of Complex Systems by Aperiodic Driving Forces, in "Quantitative Measures of Complex Dynamical Systems", N.B. Abraham (Ed.), Plenum Press, New York, 1989
    Abstract: The response of a complex system is usually very complicated if it is perturbed by a sinusoidal driving force. We show, however, that for every complex system there is a special periodic driving force which produces a simple response. This special driving force is related to a certain nonlinear differential equations. We propose to use the parameters of this differential equation to describe the complexity of the system.

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15. T. Meyer, A. Hübler, N.H. Packard, Reduction of Complexity by Optimal Driving Forces, in Quantitative Measures of Complex Dynamical Systems, N.B. Abraham (ed.), Plenum Press, New York, 352-256 (1989)
    Abstract: In general nonlinear waves are not stable in a chain of finite length. Since they have a finite lifetime, it is important to investigate the production of nonlinear waves, e.g. the production of solitons. A general feature of nonlinear waves is the amplitude frequency coupling, which causes the excitation by sinusoidal driving forces to be very inefficient. The response is usually very complex in addition. We present a method to calculate special aperiodic driving forces, which generates nonlinear waves very efficiently. The response to these driving forces is very simple.

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