Stability of cellular automata trajectories revisited : branching walks and Lyapunov profiles
- Author
- Jan Baetens (UGent) and Janko Gravner
- Organization
- Abstract
- We study non-equilibrium defect accumulation dynamics on a cellular automaton trajectory: a branching walk process in which a defect creates a successor on any neighborhood site whose update it affects. On an infinite lattice, defects accumulate at different exponential rates in different directions, giving rise to the Lyapunov profile. This profile quantifies instability of a cellular automaton evolution and is connected to the theory of large deviations. We rigorously and empirically study Lyapunov profiles generated from random initial states. We also introduce explicit and computationally feasible variational methods to compute the Lyapunov profiles for periodic configurations, thus developing an analog of Floquet theory for cellular automata.
- Keywords
- GROWTH, EXPONENTS, UNIVERSALITY, PERIODICITY, BEHAVIOR, CHAOS, SEEDS, Asymptotic shape, Branching walk, Cellular automaton, Doubly periodic, configuration, Large deviations, Lyapunov exponent, Percolation, Stability
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8510176
- MLA
- Baetens, Jan, and Janko Gravner. “Stability of Cellular Automata Trajectories Revisited : Branching Walks and Lyapunov Profiles.” JOURNAL OF NONLINEAR SCIENCE, vol. 26, no. 5, 2016, pp. 1329–67, doi:10.1007/s00332-016-9307-8.
- APA
- Baetens, J., & Gravner, J. (2016). Stability of cellular automata trajectories revisited : branching walks and Lyapunov profiles. JOURNAL OF NONLINEAR SCIENCE, 26(5), 1329–1367. https://doi.org/10.1007/s00332-016-9307-8
- Chicago author-date
- Baetens, Jan, and Janko Gravner. 2016. “Stability of Cellular Automata Trajectories Revisited : Branching Walks and Lyapunov Profiles.” JOURNAL OF NONLINEAR SCIENCE 26 (5): 1329–67. https://doi.org/10.1007/s00332-016-9307-8.
- Chicago author-date (all authors)
- Baetens, Jan, and Janko Gravner. 2016. “Stability of Cellular Automata Trajectories Revisited : Branching Walks and Lyapunov Profiles.” JOURNAL OF NONLINEAR SCIENCE 26 (5): 1329–1367. doi:10.1007/s00332-016-9307-8.
- Vancouver
- 1.Baetens J, Gravner J. Stability of cellular automata trajectories revisited : branching walks and Lyapunov profiles. JOURNAL OF NONLINEAR SCIENCE. 2016;26(5):1329–67.
- IEEE
- [1]J. Baetens and J. Gravner, “Stability of cellular automata trajectories revisited : branching walks and Lyapunov profiles,” JOURNAL OF NONLINEAR SCIENCE, vol. 26, no. 5, pp. 1329–1367, 2016.
@article{8510176,
abstract = {{We study non-equilibrium defect accumulation dynamics on a cellular automaton trajectory: a branching walk process in which a defect creates a successor on any neighborhood site whose update it affects. On an infinite lattice, defects accumulate at different exponential rates in different directions, giving rise to the Lyapunov profile. This profile quantifies instability of a cellular automaton evolution and is connected to the theory of large deviations. We rigorously and empirically study Lyapunov profiles generated from random initial states. We also introduce explicit and computationally feasible variational methods to compute the Lyapunov profiles for periodic configurations, thus developing an analog of Floquet theory for cellular automata.}},
author = {{Baetens, Jan and Gravner, Janko}},
issn = {{0938-8974}},
journal = {{JOURNAL OF NONLINEAR SCIENCE}},
keywords = {{GROWTH,EXPONENTS,UNIVERSALITY,PERIODICITY,BEHAVIOR,CHAOS,SEEDS,Asymptotic shape,Branching walk,Cellular automaton,Doubly periodic,configuration,Large deviations,Lyapunov exponent,Percolation,Stability}},
language = {{eng}},
number = {{5}},
pages = {{1329--1367}},
title = {{Stability of cellular automata trajectories revisited : branching walks and Lyapunov profiles}},
url = {{http://doi.org/10.1007/s00332-016-9307-8}},
volume = {{26}},
year = {{2016}},
}
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