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Short period attractors and non-ergodic behavior in the deterministic fixed energy sandpile model

Franco Bagnoli·Fabio Cecconi·Alessandro Flammini·Alessandro Vespignani
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Abstract

We study the asymptotic behaviour of the Bak, Tang, Wiesenfeld sandpile automata as a closed system with fixed energy. We explore the full range of energies characterizing the active phase. The model exhibits strong non-ergodic features by settling into limit-cycles whose period depends on the energy and initial conditions. The asymptotic activity $ρ_a$ (topplings density) shows, as a function of energy density $ζ$, a devil's staircase behaviour defining a symmetric energy interval-set over which also the period lengths remain constant. The properties of $ζ$-$ρ_a$ phase diagram can be traced back to the basic symmetries underlying the model's dynamics.

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Franco Bagnoli, Fabio Cecconi, Alessandro Flammini, Alessandro Vespignani. 2003-09-19. Short period attractors and non-ergodic behavior in the deterministic fixed energy sandpile model. https://doi.org/10.1209/epl%2Fi2003-00561-8

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