Three cellular automaton (CA) models of increasing complexity are introducedto model driven diffusive systems related to the generalized Frenkel-Kontorova(FK) models recently proposed by Braun [Phys.Rev.E58, 1311 (1998)]. The modelsare defined in terms of parallel updating rules. Simulation results arepresented for these models. The features are qualitatively similar to thosemodels defined previously in terms of sequentially updating rules. Essentialfeatures of the FK model such as phase transitions, jamming due to atoms in theimmobile state, and hysteresis in the relationship between the fraction ofatoms in the running state and the bias field are captured. Formulating interms of parallel updating rules has the advantage that the models can betreated analytically by following the time evolution of the occupation on everysite of the lattice. Results of this analytical approach are given for the twosimpler models. The steady state properties are found by studying the stablefixed points of a closed set of dynamical equations obtained within theapproximation of retaining spatial correlations only upto two nearestneighboring sites. Results are found to be in good agreement with numericaldata.
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