HYSTERESIS AND RETURN-POINT MEMORY IN DETERMINISTIC CELLULAR-AUTOMATA

We have investigated hysteresis and the return-point memory (RPM) prop erty in deterministic cellular automata with avalanche dynamics. The R PM property reflects a partial ordering of metastable states, preserve d by the dynamics. Recently, Sethna et al. [Phys. Rev. Lett. 70, 3347 (1993)] proved this behavior for a homogeneously driven system with st atic disorder. This Letter shows that the partial ordering and the RPM can be displayed as well by systems driven heterogeneously, as a resu lt of its own evolution dynamics. In particular, we prove the RPM prop erty for a deterministic 2D sandpile automaton driven at a central sit e.