Study of spatially distributed dynamical systems using probabilistic cellular automata

Distributed dynamical systems are ubiquitous and include such things as ins ect and animal populations; complex chemical, technological, and geochemica l processes; humanity itself, and much more. It is clearly desirable to hav e a certain universal tool with which the highly complex behaviour of nonli near dynamical systems can be analyzed and modeled. For this purpose, cellu lar automata seem to be good candidates. In the present review, emphasis is placed on the possibilities that various types of probabilistic cellular a utomata (PCA), such as DSMC (direct simulation Monte Carlo) and LGCA (latti ce-gas cellular automata), offer. The methods are primarily designed for mo deling spatially distributed dynamical systems with inner fluctuations acco unted for. For the Willamowski-Rossler and Oregonator models, PCA applicati ons to the following problems are illustrated: the effect of fluctuations o n the dynamic performance of nonlinear systems; Turing pattern formation; t he effect of hydrodynamic modes on the behaviour of nonlinear chemical syst ems (mixing effect); bifurcation changes in the dynamical regimes of comple x systems under limited-mobility low-space-dimensionality conditions; and t he description of microemulsion chemical systems.