Investigation of properties of processes characterized by logistic curves, using probabilistic cellular automata

One of the most successful processes studied is the development of systems that are either limited in area (populations), have limited development potential (technologies), or are associated with a small market size (product producers). These processes have a similar mathematical description, which involves constructing the corresponding logistic curves. Despite the obvious external differences between the listed processes, their underlying similarities are revealed through the cybernetic approach. The processes of development of biological, technical, and economic systems, which are described using C-shaped curves with the resources limited, testify to the cybernetic nature of the interaction mechanism within these systems. Aim. The paper aims to identify system-wide patterns and mechanisms of development under limited resources. Research methods. A one-dimensional probabilistic cellular automaton has been used to study developmental processes under resource constraints. The automata, which possess a scalar degree of development, compete for shared resources. Result. The use of one-dimensional cellular automata allowes us to easily obtain interpretable results and analyze the impact of different dominance conditions on the internal diversity of the system. Conclusions. The analysis of the structures allows to identify the dependence of the internal diversity of the system on the choice of dominant representatives during the competition for resources. In addition, the study predicts regarding the nature of changes in the system's structure under conditions not only of internal constraints, but also of the presence of another system that implements the "predator-prey" relationship.