Event-Based and Agent-Based Modeling

The analysis and design of complex systems in a wide variety of fields requires a modeling stage. Agent-based models are becoming more widespread, the dynamics of which is determined by the result of the individual activity of agents. And the global rules and laws of the entire system are a consequence of this activity. The lack of a formal mathematical apparatus for agent-based modeling generates a wide variety of approaches to the implementation of modeling systems and, as a result, to an ambiguous assessment of the quality of modeling systems and the results of analysis based on them. The paper proposes a matrix model for the analysis of agent systems. The significant similarity of this formalization with the classical matrix apparatus makes it possible to use well-developed mathematical methods of matrix mathematics and apply them to solve problems of parallel interaction of a large number of objects.