Structural modeling of a forest cluster using discrete mathematics

Northern (Arctic) Federal University named after M.V. Lomonosov, Severnaya Dvina Emb., 17, Arkhangelsk, 163000, Russia

^* Corresponding author: osushko@mail.ru

Abstract

Economic modeling allows studying the development trends of clusters and planning the introduction of control actions in this socio-economic system to achieve the necessary stabilization and development trends. The cluster can be described as a set of information about its elements and the relationships between them and can be represented as a graph, where the vertices are the agents, and the directed edges are connections between them. Cluster structural formations can be considered as social graphs containing information about heterogeneous factors and the relations between them. Complex structural modeling of the forest cluster allows creating a formal representation of the tasks of identifying the objects (socio-economic systems), analyzing their complexity, coherence, stability, and development scenarios. To do this, we applied the apparatus of discrete mathematics. Signed graphs make it possible to formally make forecasts of the development or trajectory of the simulated system in the phase space of its variables (factors) based on information about its structure and development programs by means of approximating them with pieces of trajectories of impulse processes in signed digraphs. Modeling with the help of the graph theory makes it possible to remove uncertainty associated with predicting the development of a complex system and to propose the option of controlling a stochastic process.