Functioning modes of asynchronous cellular automata simulating nonlinear spatial dynamics

The shift of scientific interest from physical phenomena obeying laws of thermodynamics towards nonlinear dissipative processes containing chemical and biological transformations stimulates a similar turn in mathematical modeling: from differential equation solution to direct and stochastic simulation. A foundation for discrete simulation is the asynchronous cellular automaton – a stochastic analogue of von-Neumann's cellular automaton. For the time being, there is no systematic methodology for constructing asynchronous cellular automata simulating processes composed of many actions transforming a common discrete space. It is not known, how different are simulation results obtained by different ways of composing simple operations for organizing a complex computational process. In the paper, an attempt is made to answer this question by means of performing a series of simulation of three typical reaction-diffusion processes with different asynchronous modes of functioning, and comparative analysis of their evolutions and invariants. The obtained result shows that qualitative character of the process under simulation does not depend on the composition mode, and quantitative differences may be corrected.