Stochastic Cellular Automata Simulation of Oscillations and Autowaves in Reaction-Diffusion Systems

摘要

In this paper, the investigations on stochastic cellular automata models of stable oscillations and autowaves in active media are summarized to formulate a concept of stochastic cellular automaton (CA) corresponding to asynchronous СAs with probabilistic transition rules. A formal description of a stochastic CA and a stochastic CA model is given. The properties and methods of synthesis of CA models for a specified set of elementary physical and chemical transformations are described. Some possibilities of simulating autowave and oscillatory processes are demonstrated using, as an example, a carbon monoxide oxidation reaction on a platinum catalyst with surface restructuring. The CA-simulation has made it possible to reveal the range of reaction parameter values with stable oscillations of reagent concentrations and to observe autowaves on the platinum surface. Special attention is given to providing a highly efficient parallel implementation of the stochastic CA algorithm. For this, the asynchronous mode must be preliminarily transformed to a block-synchronous one. Its equivalence to the asynchronous mode is justified. This is doné for the CA reaction model by a comparative statistical analysis of the simulation results.