Publications with Abstracts by Alfred Hübler (2005)

1. * P. Melby, N. Weber, A. Hübler, Dynamics of Self-Adjusting System with Noise, Chaos 15, 033902(2005)
   Abstract: We perform studies of several self-adjusting systems with noise. In our analytical and numerical studies, we find that the dynamics of the self-adjusting parameter can be accurately described with a rescaled diffusion equation. We find that adaptation to the edge of chaos, a feature previously ascribed to self-adjusting systems, is only a long-lived transient when noise is present in the system. In addition, using analytical, numerical, and experimental studies, we find that noise can cause chaotic outbreaks where the parameter reenters the chaotic regime and the system dynamics become chaotic. We find that these chaotic outbreaks have a power law distribution in length.

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2. * J. Jun, A. Hübler, Formation and structure of ramified charge transportation networks in an electromechanical system, PNAS 102, 536–540 (2005)
   Abstract: We present findings in an experiment where we obtain stationary ramified transportation networks in a macroscopic nonbiological system. Our purpose here is to introduce the phenomenology of the experiment. We describe the dynamical formation of the network which consists of three growth stages: (I) strand formation, (II) boundary formation, and (III) geometric expansion. We find that the system forms statistically robust network features, like the number of termini and the number of branch points. We also find that the networks are usually trees, meaning that they lack closed loops; indeed, we find that loops are unstable in the network. Finally, we find that the final topology of the network is sensitive to the initial conditions of the particles, in particular to its geometry.

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3. A. Hübler, Predicting Complex Systems with a Holistic Approach, Complexity 10(3), 11-16 (2005)
   Abstract: Systems become complex if their throughput is increased beyond a certain threshold. To understand the emerging irregular patterns and dynamics, phenomenological descriptions of their behavior must be translated into computational algorithms. We illustrate that the emerging structures appear to be particularly simple if we draw the boundary of the system at a location where the inputs and outputs are controllable. Further we show that the boundary can trigger two types of pattern forming processes: one which starts at the largest scales of the system and creates structure at smaller and smaller scales, and one that starts on the smallest scales and produces structure on larger scales. Only if we use a holistic approach, by considering both the both the bottom-up and the top-down patter formation process can we understand the emerging patterns and dynamics.

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