Name
Title | ||
|---|---|---|
Stability of cellular automata trajectories revisited: branching walks and Lyapunov profiles |
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. |
Year | DOI | Venue |
|---|---|---|
2016 | https://doi.org/10.1007/s00332-016-9307-8 | J. Nonlinear Science |
Keywords | Field | DocType |
Asymptotic shape,Branching walk,Cellular automaton,Doubly periodic configuration,Large deviations,Lyapunov exponent,Percolation,Stability,60K35,37B15 | Lyapunov function,Cellular automaton,Mathematical analysis,Large deviations theory,Block cellular automaton,Periodic graph (geometry),Stochastic cellular automaton,Lyapunov exponent,Mathematics,Floquet theory | Journal |
Volume | Issue | Citations |
26 | 5 | 2 |
PageRank | References | Authors |
0.46 | 6 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jan M. Baetens | 1 | 26 | 7.65 |
| Janko Gravner | 2 | 4 | 3.64 |