Interacting random systems (some of which are known as random cellular automata) are random processes which describe the collective behavior of many components, placed in a d-dimensional discrete space and interacting with each other in a discrete or continuous time. This research will further develop the method of branching contours in order to examine the asymptotic behavior of interacting random systems, in which the set of states of a single component is infinite (a line, a circle). Computer simulation of interacting random systems will be used as a preliminary step for obtaining rigorous results. Interacting random systems (some of which are known as random cellular automata) are now often used now to simulate the behavior and properties of those real objects whose multi-component structure cannot be ignored. They are used extensively in mathematical modeling of physical, chemical, biological and other systems. The importance of interacting random systems is widely acknowledged. Computer simulations of various kinds of interacting systems now abound around the world, but rigorous results in this area are not so rich as in older branches of mathematics, because straightforward application of traditional mathematical methods brings only limited success in this new field. This research will investigate the mathematical properties of interacting random systems, especially their qualitative and asymptotic behavior using both classical methods from different areas of mathematics and those newly developed.
