Quantitative description of the dynamics of interactions of living systems


by the method of state equations

Part 1: Derivation of the equations of the predator-prey model

from the equations of state of living systems



By Pavel Barseghyan

Texas and Armenia


The mathematical theory of human systems based on equations of state is also applicable for the model representation of the interaction dynamics of living systems, including a quantitative description of the life cycle of animals and their interactions.

The reason for this is the fact that both the life of humans and animals is a sequence of various actions that can be described by equations of state.

This also means that the universal method of equations of state must be in agreement with other known quantitative models representing the life and interactions of living systems.

The only way to prove the validity of such a statement is to derive the known quantitative models of living systems and their interactions basing on the method of state equations.

In this paper, it is shown that the behavior of the predator-prey system can be described by the method of equations of state, and based on this, one can easily obtain the differential equations of the famous predator-prey model of Lotka-Volterra in an analytical way.

This means that in the same way it is possible to obtain other known quantitative laws representing the behavior of living systems.

Moreover, such an approach also can make it possible to obtain analytically new patterns representing the possible manifestations of the behavior of living systems.


All living systems, from the simplest organisms to people, society and civilization, in each situation are guided by the principle of ensuring the continuity and longevity of their life [1].

Since life at any level survives under conditions of various kinds of changes, in the event of an arbitrary change, the biosystem seeks to ensure the continuity of its life with maximum probability.

The course of life of an arbitrary biosystem is a sequence of actions, which is the response of this biosystem to the successive demands of life.

If the course of the life of a biosystem is stable and continuous, then there is a certain balance between the sequence of life requirements and the responses to these requirements on the part of the biosystem.

The concept of such a balance allows for a quantitative interpretation of the principle of continuity and longevity of life in the form of mathematical equations [1].

On the other hand, a quantitative interpretation of this principle is possible only if both the requirements of life and the responses of the biosystem to these requirements can be presented in a parametric form [2].


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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 1: Derivation of the equations of the predator-prey model from the equations of state of living systems; PM World Journal, Vol. X, Issue V, May.  Available online at https://pmworldlibrary.net/wp-content/uploads/2021/05/pmwj105-May2021-Barseghyan-equations-of-the-predator-prey-model.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/