Dresden 2009 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 9: Nonlinear dynamics, synchronization and chaos II

DY 9.1: Vortrag

Dienstag, 24. März 2009, 10:15–10:30, ZEU 255

Noise and timing in cellular automata — •Konstantin Klemm — Bioinformatics, Leipzig University, Germany

Cellular automata (CA) form a broad class of models for discrete complex dynamics as they produce a wealth of non-trivial spatio-temporal patterns with simple rules of interaction. The complex behaviour is observed in deterministic CA with step-wise synchronous update. However, long-term and long-range correlations are suppressed when switching to random asynchronous update which acts as a source of strong noise.

Here I consider CA under weak but non-vanishing noise, implemented as small fluctuations of the time a cell needs to respond to a changing input. I find that stability under these fluctuations strongly varies across CA rules. In Conway's Game of Life, most dynamic elements such as blinkers and gliders are unstable. Also Wolfram's elementary CA rule 110 is highly unstable, while the linear rule 150 and the chaotic rule 22 are examples of stable rules. These findings restrict the candidate set of mechanisms underlying complex dynamics. In the presence of noise, only stable CA rules are eligible as models of reproducible pattern generation.