Quantitative description of the dynamics of interactions of living systems


by the method of state equations

Part 3: The power of human systems and

dynamic mathematical models of their interactions



By Pavel Barseghyan

Texas and Armenia


The main topic of this article is a quantitative presentation of the dynamics of the relationship between humans and human systems through mathematical models of the predator-prey type.

This representation of human relations is based on the assertion that each human system through its activity exerts positive and negative pressure on other human systems associated with it, which can be described by equations of state.

The article examines a dynamic mathematical model of the relationship between two human systems, which is a system of two differential equations reflecting the state of the system.

With the help of such a model of human interactions, it is possible to describe the victory and defeat of human systems in the form of aperiodic solutions of differential equations, as well as the balanced life of human systems without serious shocks in the form of periodic or quasiperiodic solutions of the same differential equations.


The field of studying the interaction of human systems has traditionally been, and generally remains, the field of application of non-quantitative methods.

In the second half of the twentieth century, mainly under the influence of systems theory [1], cybernetics [2] and physics [3, 4], many attempts were made to quantify the problems of psychology, organizational science, project management, social and political sciences, geopolitical and other problems.

A characteristic feature of all these approaches is that they all adapt the ideology, methods and approaches of other areas that have reached a high level of development to the study of the life and activities of people and human systems.

But as is known from the history of science, real scientific successes and achievements in any particular field become reality only when they are based on their own philosophy, ideology, methods and approaches, which can only be born on the basis of systematic research in that specific area.

In this sense, the quantitative science of life, behavior and activity of human systems is at that stage of its development when ideological and methodological borrowings from more developed fields of science have basically completed their work, on the basis of which it became possible to develop their own approaches to the problem.

The ideological basis of this series of articles in the field of mathematical modeling of the behavior and activity of biosystems is the principle of a fundamental nature according to which any biosystem in various situations seeks to ensure the continuity, longevity and perpetuation of its life [5, 6].

This principle is very rich in its essence, on the basis of which it is possible to explain the arbitrary manifestation of the course of animal life and the activity of human systems.

Since the continuity and longevity of life, in turn, are based on the safety of life, energy supply and its reproduction, this principle is divided into three sub-principles, namely:

– a sub-principle of energy security, including maximizing energy inflow and minimizing its consumption,

– a sub-principle of ensuring the safety of life with maximum probability,

– a sub-principle of ensuring the reproduction and training of the species with maximum probability.

These three sub-principles, in turn, can have many other branches, which can cover various phenomena and processes associated with the life of biological systems and the activities of human systems.

In particular, a sub-principle of this kind is Zipf’s principle of minimum effort [7], which is a special case of the principle of minimum energy consumption, and which, among its many applications, can also cover linguistic problems [8].

In addition, the principle of minimum effort, in turn, can have its ramifications and consequences. In particular, in [9] quantitative universal laws, such as the Zipf-Pareto distributions, follow directly from the principle of minimum effort.


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How to cite this paper: Barseghyan, P. (2021). Quantitative description of the dynamics of interactions of living systems by the method of state equations – Part 3: The power of human systems and dynamic mathematical models of their interactions; PM World Journal, Vol. X, Issue VII, July. Available online at https://pmworldlibrary.net/wp-content/uploads/2021/06/pmwj107-Jul2021-Barseghyan-part-3-power-of-human-systems.pdf

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 terbpl@gmail.com

To view other works by Dr. Barseghyan that have been published in the PM World Journal, visit his author showcase in the PM World Library at https://pmworldlibrary.net/authors/dr-pavel-barseghyan/