arXiv subjects

Jens Christian Claussen

Publications and source records attributed to Jens Christian Claussen.

44 records · Page 3Linked to original sources

arXiv2005

Similarity based cooperation and spatial segregation

We analyze a cooperative game, where the cooperative act is not based on the previous behaviour of the co-player, but on the similarity between the players. This system has been studied in a mean-field description recently [A. Traulsen and H. G. Schuster, Phys. Rev. E 68, 046129 (2003)]. Here, the spatial extension to a two-dimensional lattice is studied, where each player interacts with eight players in a Moore neighborhood. The system shows a strong segregation independent on parameters. The introduction of a local conversion mechanism towards tolerance allows for four-state cycles and the emergence of spiral waves in the spatial game. In the case of asymmetric costs of cooperation a rich variety of complex behavior is observed depending on both cooperation costs. Finally, we study the stabilization of a cooperative fixed point of a forecast rule in the symmetric game, which corresponds to cooperation across segregation borders. This fixed point becomes unstable for high cooperation costs, but can be stabilized by a linear feedback mechanism.

cond-mat.stat-mech↗

arXiv2004

Winner-Relaxing Self-Organizing Maps

A new family of self-organizing maps, the Winner-Relaxing Kohonen Algorithm, is introduced as a generalization of a variant given by Kohonen in 1991. The magnification behaviour is calculated analytically. For the original variant a magnification exponent of 4/7 is derived; the generalized version allows to steer the magnification in the wide range from exponent 1/2 to 1 in the one-dimensional case, thus provides optimal mapping in the sense of information theory. The Winner Relaxing Algorithm requires minimal extra computations per learning step and is conveniently easy to implement.

cond-mat.dis-nn↗

arXiv2004

Underetching from simple stochastic etching kinetics

The morphological richness of electrochemical semiconductor etching is not sufficiently counterparted yet by theoretical modeling. This paper investigates a minimal version of the Current-Burst model with Aging of Föll and Carstensen and demonstrates for a restricted geometry that the Aging concept is essential for underetching, or cavity generation. If the influence of Aging is neglected, the dynamics reduces to a Random Etching Model similar to the Random Deposition model. This computer {\sl gedanken experiment} demonstrates that the stochastic dynamics with ageing-dependent kinetic reaction probabilities accounts for the different etching morphologies compared to those obtained in surface roughening and related systems.

cond-mat.mtrl-sci↗

arXiv2004

Time-evolution of the Rule 150 cellular automaton activity from a Fibonacci iteration

The total activity of the single-seeded cellular rule 150 automaton does not follow a one-step iteration like other elementary cellular automata, but can be solved as a two-step vectorial, or string, iteration, which can be viewed as a generalization of Fibonacci iteration generating the time series from a sequence of vectors of increasing length. This allows to compute the total activity time series more efficiently than by simulating the whole spatio-temporal process, or even by using the closed expression.

math.CO↗

arXiv2004

$1/f^α$ spectra in elementary cellular automata and fractal signals

We systematically compute the power spectra of the one-dimensional elementary cellular automata introduced by Wolfram. On the one hand our analysis reveals that one automaton displays $1/f$ spectra though considered as trivial, and on the other hand that various automata classified as chaotic/complex display no $1/f$ spectra. We model the results generalizing the recently investigated Sierpinski signal to a class of fractal signals that are tailored to produce $1/f^α$ spectra. From the widespread occurrence of (elementary) cellular automata patterns in chemistry, physics and computer sciences, there are various candidates to show spectra similar to our results.

nlin.CG↗

arXiv2004

Improved control of delayed measured systems

In this paper we address the question how the control of delayed measured chaotic systems can be improved. Both unmodified OGY control and difference control can be successfully applied only for a certain range of Lyapunov numbers depending on the delay time. We show that this limitation can be overcome by at least two classes of methods, by rhythmic control and by the memory methods linear predictive logging control (LPLC) and memory difference control (MDC).

chao-dyn↗

arXiv2004

Stability borders of feedback control of delayed measured systems

When stabilization of unstable periodic orbits or fixed points by the method given by Ott, Grebogi and Yorke (OGY) has to be based on a measurement delayed by $τ$ orbit lengths, the performance of unmodified OGY method is expected to decline. For experimental considerations, it is desired to know the range of stability with minimal knowledge of the system. We find that unmodified OGY control fails beyond a maximal Ljapunov number of $λ_{max}=1+\frac{1}τ$. In this paper the area of stability is investigated both for OGY control of known fixed points and for difference control of unknown or inaccurately known fixed points. An estimated value of the control gain is given. Finally we outline what extensions have to be considered if one wants to stabilize fixed points with Ljapunov numbers above $λ_{max}$.

nlin.CD↗

arXiv2004

Sierpinski signal generates $1/f^α$ spectra

We investigate the row sum of the binary pattern generated by the Sierpinski automaton: Interpreted as a time series we calculate the power spectrum of this Sierpinski signal analytically and obtain a unique rugged fine structure with underlying power law decay with an exponent of approximately 1.15. Despite the simplicity of the model, it can serve as a model for $1/f^α$ spectra in a certain class of experimental and natural systems like catalytic reactions and mollusc patterns.

cond-mat.stat-mech↗