Quantitative description of the dynamics of interactions of living systems


by the method of state equations

Part 2: Productivity Gap vs. Investments:

Quantitative analysis based on predator-prey model and state equations



By Pavel Barseghyan

Texas and Armenia


In the process of development, human activity moves from one paradigm of its implementation to another, more effective in terms of human productivity.

In this sense, in the process of development, each paradigm is characterized by its own potential capabilities, which are gradually being exhausted, and this leads to the fact that a dynamic gap between the needs of life and the capabilities of people is gradually growing, the bridging of which requires new investments.

In this sense, the normal development process is the sum of interconnected processes of periodic changes in the dynamic gap in human productivity and investments aimed at bridging this gap.

This article is devoted to the construction of mathematical models of the above-mentioned periodic processes using two different approaches.

The first approach looks at productivity gaps and investment processes with the aim of closing them in terms of the well-known predator-prey model.

The second approach to the same problem is based on the method of dynamic equations of state, the resulting model of which coincides with the results of the first approach, which indicates the great possibilities of practical applications of the method of equations of state.


One of the main trends in human history and the development of society is a systematic increase in human labor productivity, based on targeted investments of society.

Progress in any area of human endeavor is usually accompanied by a range of financial, governmental and geopolitical considerations aimed at achieving or maximizing an overall competitive advantage or generalized benefit.

Here, the generalized benefit is understood as the entire spectrum of material and non-material interests of people, their various combinations depending on the value system of a particular human or social unit.

Often, depending on the circumstances, the desire of people to maximize the generalized gain is replaced by their desire to minimize the generalized loss, which is more applicable to processes of a regression type.

Any progress is based on the dissatisfaction of people or society with the current situation, which is measured by the difference between the size of society’s demand and the real capabilities of the human system that implements it.

If, along with this discontent, society has the opportunity to overcome it in the form of the resources and abilities of people, then together with a certain ideology with a tendency to progress, all this can serve as a basis for investing in a specific direction.

From this point of view, the degree of dissatisfaction mentioned above can be expressed as the difference between the desired or potential performance of people in a particular area and their actual performance, which is called the productivity gap [1].

Thus, the dynamics of the development of any sphere of human activity can be represented as a process of interaction and mutual conditionality of the gap in productivity and investments aimed at eliminating it.

A qualitative picture of this process can be presented in the following simplified form.


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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 2: Productivity Gap vs. Investments: Quantitative analysis based on predator-prey model and state equations; PM World Journal, Vol. X, Issue VI, June.  Available online at https://pmworldlibrary.net/wp-content/uploads/2021/06/pmwj106-Jun2021-Barseghyan-part-2-productivity-gap-vs-investments-quantitative-analysis.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/