Abstract
Manyappliedtasksaresimulatedbydifferenceequationsthatdescribethevectorofsystemstatesevolutionintime. Howeveritisrequiredtotakeintoaccount the spatial structure of simulated processes or systems in some tasks. Inpaperthepossibilityofaspatio-temporalprocessessimulation by cellular automata is considered. The brief review of two-dimensional cellular automataproperties is provided.Theprincipleofthemostfamoustwo-dimensionalcellularautomata“Game of Life”is described.Alsothegeneralwaytosettheseautomatainananalyticalformby Reaction-Diffusion equation is considered. Concrete forms of the Reaction equation and Diffusion equation are constructed and invariant sets for this system are defined. Thegeneralizationofanalyticalcellularautomata representation in total is provided.Asanexample,themodelofpopulationdevelopmentisconsidered. ItutilizestheclassicFerhulstequation, inwhichthespatialstructureistakenintoaccounthavingformofthecumulativeneighbors’impactonpopulationchangesrate.As per using of analytical form of cellular automata, differentschemasofsystemspatio-temporalcharacteristicscontrol aresuggested. Theseschemasarebasedonfeedback: delayedfeedback(thatis one that uses previous system states)and predictive feedback (that is one that uses predicted system states). As aresultthereismanaged to synchronize spatial configuration of cellular automataand it can be interpreted as stable population development. Particularly, cellular automata could work in cycle with cycle length set earlier. For cellular automata evolution visualization the algorithms and their computer implementation aredeveloped.Discrepancy functionis suggested, due to which it is possible to evaluate the synchronization accuracy. Research results and examples of received configurations are presented.
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