Stochastic cellular automata simulation of oscillations and autowaves in reaction-diffusion systems

O. L. Bandman ; A. E. Kireeva

Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 18 (2015) no. 3, pp. 255-274.

Résumé

In this paper, experience in the conducted investigation of the stochastic cellular automata models of forming stable oscillations and autowaves in active media is generalized. As a result, the concept of stochastic cellular automaton (CA), corresponding to the asynchronous CA with probabilistic transition rules, is formulated. The formal notions of a stochastic CA and a stochastic CA model are given. Properties of the CA models and methods of their synthesis, using a specified set of elementary physical and chemical transformations, are described. The possibility of the autowave and oscillatory processes simulation is shown on an example of the carbon monoxide oxidation reaction on the platinum catalyst with reconstructing its surface structure. The CA-simulation enabled to reveal the range of reaction parameters values, at which stable oscillations of the reagents concentration occur, and to observe autowaves over the platinum surface. Considerable attention has been given to a high efficiency of the stochastic CA parallel implementation, which demands preliminary transformation of the asynchronous mode to the block-synchronous one with validation of its equivalence to the asynchronous mode. The latter is done for the investigated reaction CA model by means of the comparative statistical analysis of the simulation results.

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