Abstract
We show that a time series evolving by a nonlocal update rule with two different delays can be mapped onto a local process in two dimensions with special time-delayed boundary conditions, provided that and are coprime. For certain stochastic update rules exhibiting a nonequilibrium phase transition, this mapping implies that the critical behavior does not depend on the short delay . In these cases, the autocorrelation function of the time series is related to the critical properties of the corresponding two-dimensional model.
1 More- Received 28 March 2007
DOI:https://doi.org/10.1103/PhysRevE.77.031106
©2008 American Physical Society