10.46298/dmtcs.2974
https://dmtcs.episciences.org/2974
Perrot, Kévin
Kévin
Perrot
Phan, Thi Ha Duong
Thi Ha Duong
Phan
Pham, Trung Van
Trung Van
Pham
On the set of Fixed Points of the Parallel Symmetric Sand Pile Model
Sand Pile Models are discrete dynamical systems emphasizing the phenomenon of $\textit{Self-Organized Criticality}$. From a configuration composed of a finite number of stacked grains, we apply on every possible positions (in parallel) two grain moving transition rules. The transition rules permit one grain to fall to its right or left (symmetric) neighboring column if the difference of height between those columns is larger than 2. The model is nondeterministic and grains always fall downward. We propose a study of the set of fixed points reachable in the Parallel Symmetric Sand Pile Model (PSSPM). Using a comparison with the Symmetric Sand Pile Model (SSPM) on which rules are applied once at each iteration, we get a continuity property. This property states that within PSSPM we can't reach every fixed points of SSPM, but a continuous subset according to the lexicographic order. Moreover we define a successor relation to browse exhaustively the sets of fixed points of those models.
episciences.org
Discrete Dynamical System
Sand Pile Model
Fixed point
[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
[MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]
[NLIN.NLIN-CG] Nonlinear Sciences [physics]/Cellular Automata and Lattice Gases [nlin.CG]
[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]
2023-03-28
2011-01-01
2011-01-01
en
journal article
https://hal.science/hal-01196141v1
1365-8050
https://dmtcs.episciences.org/2974/pdf
VoR
application/pdf
Discrete Mathematics & Theoretical Computer Science
DMTCS Proceedings vol. AP, Automata 2011 - 17th International Workshop on Cellular Automata and Discrete Complex Systems
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