A Discrete Dynamic Conflict Model

Abstract

Relevance. Conflicts play a significant role in the development of society, the state and all of humanity. They arise in interpersonal relationships, economics, organizational activities, social problems, and world politics. The study of the essence of conflicts, the causes of their emergence and ways to resolve them is carried out by conflictology, which was formed as an interdisciplinary field of knowledge in the middle of the 20th century. Currently, it has become obvious that the conflict itself is not a negative phenomenon, but a competently resolved conflict situation can benefit all parties to the conflict. As a result, it became necessary to consider conflicts not only from a descriptive, philosophical point of view, but also to be able to predict a possible conflict situation, describe its development over time and calculate acceptable ways out of it. This approach to the study of conflicts is mathematical modeling, based on mathematical methods for describing conflict situations, which allow analyzing conflicts and predicting their outcome.The purpose is to describe a general methodology for constructing a conflict scheme of any origin within the framework of the mathematical theory of conflicts. The objectives is to consider and analyze a discrete dynamic model of conflicts using the example of a childparent conflict.Methodology. The work uses algebraic methods and methods of discrete mathematics.Results. Within the framework of the mathematical theory of conflicts, a conflict with a discrete mismatch is considered the example of a child-parent model conflict. A general method for constructing a conflict situation diagram and analyzing it has been developed. Possible ways of influencing the conflicting parties on each other in any conflict situation are discussed. When analyzing possible scenarios for the development of a conflict situation, the possible types of impacts of the conflicting parties on each other are considered.Conclusions. Based on the developed dynamic discrete model, it is shown that the mathematical description of conflicts is reduced to the problem of combinatorial optimization. The developed scheme of mathematical description of conflicts can be applied to a wide class of conflict situations in various subject areas.