Elements of the Mathematical Theory of Human Systems, Part 5

Quantitative analysis of the benefits and losses of two human systems in the regime of confrontational equilibrium of their interrelations



By Pavel Barseghyan, PhD

Yerevan, Armenia and

Plano, Texas, USA



Quantitative analysis of confrontation and acute conflict situations between human systems makes it possible to evaluate and predict the results of different scales of collisions between people in the form of potential benefits and losses.

From the point of view of an adequate quantitative representation of the confrontation between human systems, it is advisable to use such parameters and notions that are universal in nature and invariant with respect to the systems under study.

In other words, these models should operate with universal concepts such as stability and equilibrium of the state of the system, conflict of interests of the opposing sides, the magnitude of the expected benefits, losses and mutual concessions, and so on, which are characteristic of all opposing and conflicting human systems.

Like other activities carried out by people, the process of conflicts between them is also a certain sequence of their mutual actions, which can be quantitatively described by the equations of state of opposing human systems.

This article is devoted to the qualitative and quantitative assessment of losses arising as a result of the conflict between two human systems.

In the first part of the research, the graphic analysis of the process and results of the conflict are carried out, and the second part is devoted to the development of linear and nonlinear mathematical models of confrontation between people and their losses.

Mathematical models of confrontation of two human systems, presented in this article, will later become a platform for quantitative modeling of more complex situations in the clash of three or more conflicting parties.

Key words: Human systems, mathematical theory, state equations, equilibrium, non-equilibrium, benefits, losses, conflicts, confrontational equilibrium, interrelations, pressure on human systems, upper limits of mutual pressure, power of human systems


To ensure the safety, prosperity and sustainable development of human systems, a comprehensive quantitative analysis of the equilibrium and non-equilibrium states of their interactions is necessary [1].

The method of equations of state of human systems is a convenient tool for the practical realization of this goal, namely the representation of the relationships between these systems in the form of a system of equations of states, where each of these equations reflects the behavior of the relationships between the two of these systems.

In addition, in modeling, it should be taken into account that the interactions between pairs of human systems are not symmetrical, and for this reason, the mutual influences of the parties are represented by separate equations, each of which splits into two equations, one of which presents a positive pressure on the opposite side, and the other – negative pressure on the same opposite side.

Thus, the mathematical model of the relationship between each pair of interacting human systems in the general case is a system of four equations of state.

This means that with the increase in the number of human systems , the number of equations of state of their mutual relations will increase sharply and in the case  for this purpose we will have 12 equations, and in the case  we will deal with 24 equations.

In addition, since the pressure on each side of the confrontation can be divided into different types of pressures, such as political pressure, economic pressure, financial pressure, etc., the number of equations representing the state of human relations can be increased even more rapidly.

Naturally, under such conditions, the targeted use of the behavioral models under consideration based on a large number of state equations representing the relationships between human systems is possible only within the framework of modern expert information systems.

On the other hand, in cases where the relationships between human systems are only of a confrontational nature or only the nature of cooperation, the number of equations in the corresponding models can be reduced by half.

From a practical point of view, mathematical modeling of the relationships between the three human systems is of great interest, since this case is relatively simple from the mathematical point of view, but it is already quite complex in the meaningful sense.

In particular, in this case it is already possible to make an object of quantitative consideration the problems of the emergence and degradation of coalitions of people (important from the point of view of the productivity of design teams), organizations (important from the point of view of business) and countries (important from the geopolitical point of view).

In any case, a quantitative analysis of the relationships of an arbitrary number of human systems is based on models of interaction between two human systems that are the subject of further consideration.


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About the Author

Pavel Barseghyan
, PhD

Yerevan, Armenia
Plano, Texas, USA



Dr. Pavel Barseghyan is a consultant in the field of quantitative project management, project data mining and organizational science. Has over 45 years’ experience in academia, the electronics industry, the EDA industry and Project Management Research and tools development. During the period of 1999-2010 he was the Vice President of Research for Numetrics Management Systems. Prior to joining Numetrics, Dr. Barseghyan worked as an R&D manager at Infinite Technology Corp. in Texas. He was also a founder and the president of an EDA start-up company, DAN Technologies, Ltd. that focused on high-level chip design planning and RTL structural floor planning technologies. Before joining ITC, Dr. Barseghyan was head of the Electronic Design and CAD department at the State Engineering University of Armenia, focusing on development of the Theory of Massively Interconnected Systems and its applications to electronic design. During the period of 1975-1990, he was also a member of the University Educational Policy Commission for Electronic Design and CAD Direction in the Higher Education Ministry of the former USSR. Earlier in his career he was a senior researcher in Yerevan Research and Development Institute of Mathematical Machines (Armenia). He is an author of nine monographs and textbooks and more than 100 scientific articles in the area of quantitative project management, mathematical theory of human work, electronic design and EDA methodologies, and tools development. More than 10 Ph.D. degrees have been awarded under his supervision. Dr. Barseghyan holds an MS in Electrical Engineering (1967) and Ph.D. (1972) and Doctor of Technical Sciences (1990) in Computer Engineering from Yerevan Polytechnic Institute (Armenia).  Pavel’s publications can be found here: http://www.scribd.com/pbarseghyan and here: http://pavelbarseghyan.wordpress.com/.  Pavel can be contacted at [email protected]