Publications with Abstracts by Alfred Hübler (2006)

1. ^* M. Baym, A. Hübler, Self-adjusting Dynamical Systems with Wavelet Filtered Feedback, Phys. Rev. E 73, 056210-1-7 (2006).
   Abstract: Certain dynamical systems, such as the shift map and the logistic map, have an edge of chaos in their parameter spaces. On one side of this edge, the dynamics are chaotic for many parameter values, on the other side of the edge they are periodic. We find that discrete-time dynamical systems with wavelet-filtered feedback from the dynamical variable to the parameters are attracted to a narrow parameter range near the edge of chaos, the periodic boundary regime. We show that the migration from the chaotic regime to the periodic boundary regime can be attributed to a conserved quantity, and find that such adaptation to the edge of chaos is accompanied by a depopulation of the chaotic regime. We use this conserved quantity to determine the location of the periodic boundary regime and show that its size is proportional to the size of the feedback. Further, we compute the dynamics of the probability density for the parameter for a specific example.

   Preprint

2. ^*C. Strelioff, A. Hübler, Medium-Term Prediction of Chaos, PRL 96, 044101 (2006)
   Abstract: We study prediction of chaotic time series when a perfect model is available but the initial condition is measured with uncertainty. A common approach for predicting future data given these circumstances is to apply the model despite the uncertainty. In systems with fold dynamics, we find prediction is improved over this strategy by recognizing this behavior. A systematic study of the logistic map demonstrates prediction of the most likely trajectory can be extended three time steps. Finally, we discuss application of these ideas to the Rössler attractor.

   Reprint

3. A. Hübler, G. C. Foster, How to create a large response from chaotic systems: Optimal forcing functions complement the natural dynamics of a system, Complexity 11(4), 11-13 (2006)

   Preprint

4. ^*K. Phelps, A. Hübler, Towards an understanding of membership in youth organizations: Sudden changes in the average participation due to the behavior of one individual, Emergence, Complexity, and Organization 8, 30-37 (2006).
   Abstract: Peer pressure can induce sudden unexpected changes in the behavior of a group. With agent based simulations we study impact of one individual on the behavior of a social network of people. We find that the individual with the largest benefit dominates the group behavior. If that individual happens to have a leadership role, the impact is particularly strong. The model suggests that even if the average benefits for the group changes slowly the average participation changes suddenly and with a delay. The delay is shorter if the network is subject to large unpredictable outside influences. Further we find that incentives which target leaders are more effective than unspecific incentives. We discuss applications of the model to the dynamics of membership in agricultural youth organization.

   Preprint

5. A. Hübler, A. Vlasic, E. Stiegler, L. Bievenue, D. Raineri, Interactive Middle School Courseware on Abstract Reasoning Skills, in C. Crawford et al. (Eds.), Proceedings of Society for Information Technology and Teacher Education International Conference 2006 (AACE: Chesapeake, VA, 2006) pp 389-394.
   Abstract:Quantitative reasoning skills are a fundamental tool in many fields, ranging from Mathematics to Engineering and from Business to Rhetoric. However, quantitative reasoning is almost never taught as a course, except in the context of other disciplines, such as Mathematics or Physics. We introduce basic elements of a course in reasoning, such as the definition of a concept and the definition of a strategy and study the response of the students. We apply the definitions to algebraic proofing. We conceptualize algebraic concepts, i.e. we name each concept, define its range of applicability and illustrate each concept with typical examples. We also conceptualize strategies for proofing. We find that a diverse population of female middle school students readily accepts this approach and achieves proofing skills on a level which is comparable to university freshmen.

   Preprint

6. G. Foster, A. Hübler, K. Dahmen, Resonance Spectroscopy with Chaotic Forcing Functions, Preprint (2006)
   Abstract: We study resonance curves of nonlinear dynamical systems with chaotic forcing functions. We use the calculus of variations to determine the forcing function that induces the largest response. We find that the product of resonant forcing and the displacement of nearby trajectories is a conserved quantity, i.e. when the displacement dynamics is irregular, the resonant forcing function is irregular too. We compute the resonant forcing for a set of model systems and determine the response of the dynamical system to each forcing function. We show that the response is largest if the model system matches the dynamical system. We find that the signal to noise ratio is particularly large if one of the Lyapunov exponents is large.

   Preprint

7. A. Hübler, Information engines: Converting information into energy, Complexity 12(2), 10-12(2006)

   Preprint