Many applied tasks are simulated by difference equations that describe the vector of system states evolution in time. However it is required to take into account the spatial structure of simulated processes or systems in some tasks. In paper the possibility of a spatio-temporal processes simulation by cellular automata is considered. The brief review of two-dimensional cellular automata properties is provided. The principle of the most famous two-dimensional cellular automata “Game of Life” is described. Also the general way to set these automata in an analytical form by Reaction-Diffusion equation is considered. Concrete forms of the Reaction equation and Diffusion equation are constructed and invariant sets for this system are defined. The generalization of analytical cellular automata representation in total is provided. As an example, the model of population development is considered. It utilizes the classic Ferhulst equation, in which the spatial structure is taken into account having form of the cumulative neighbors’ impact on population changes rate. As per using of analytical form of cellular automata, different schemas of system spatio-temporal characteristics control are suggested. These schemas are based on feedback: delayed feedback (that is one that uses previous system states) and predictive feedback (that is one that uses predicted system states). As a result there is managed to synchronize spatial configuration of cellular automata and 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 are developed. Discrepancy function is suggested, due to which it is possible to evaluate the synchronization accuracy. Research results and examples of received configurations are presented.

In many decisionsupport systemsthere are processedchaotic spatial-time processes which are non-separable and quasi-periodic. Some examples of such systemsareepidemic spreading, population development, fire spreading, radio wave signals, image processing, information encryption, radio vision, etc. Processes in these systems have periodic character, e.g. seasonal fluctuations(epidemic spreading, population development), harmonic fluctuations (pattern recognition, image processing),etc. In simulation block the existing systems use separable process models which are presented as multiplication of spatialand temporal parts and are linearized. This significantly reduces the quality of spatial-time non-separable processes. The quality model building of chaotic spa-tial-time non-separable processwhich is processed by decisionsupport systemis necessary for getting of learning set. Itis really complicated especially if the random process is formed. The implementation ensemble of chaotic spatial-time non-separable process requires high costs what causes reduction of the system efficiency. Moreover, in many cases the implementation ensemble of spatial-time processes is impossible to get. In this workthemathematical model of a quasi-periodic spatial-time non-separable process has been developed. Based on it the formation method of this process has been developed and investigated. The epidemic spreading pro-cessed was presented as an example

Одесский национальный политехнический университет Аннотация. Рассматривается проблема представления клеточных автоматов в виде разностных уравнений. Для этого строится система типа Диффузия-Реакция. При этом, уравнение Реакции представляется как отображение сумм функций «тент». Такое представление позволяет рассматривать клеточные автоматы с произвольным конечным или бесконечным числом состояний. Построена модель линейных клеточных автоматов, действующих по правилам кода Вольфрама [1]. Приведены примеры. Ключевые слова: клеточные автоматы, дискретные динамические системы, контроль, периодические решения.