Complex system self-organization and boundary of its perception

Yu. Dubrov, A. N. Tkachenko


Stipulations. The term “complex system” (CS) is rather frequently utilized, therefore, we will take an effort to give a detailed explanation of what is understood by this term. In order to do that, we will not cite a variety of interpretations existing for this term, instead, we are intended to give a notion to this term that would provide for a more visual interpretation. Basic problem statement. Using the abovementioned Stipulation and Hypotheses it is necessary to determine a quality criterion of a self-organizing system functioning as well as to give its formal description. Certain SC subclasses. In order to detect qualitative peculiarities of the considered model the following numerical investigations were conducted. In a new equilibrium state we obtain an absolutely new evolvable system that again, with the change of a load parameter, initiates the process of its development similar. Facts confirming presence of information perception boundary (IPB) with self-organizing systems. Given analysis shows that any system, capable of perceiving information, possesses its own IPB. This fact comes well enough to an agreement with data that prove the possibilities of self-organization on the basis of the existing principles of physics and biology. According to the abovementioned it can be concluded that the task of a qualitative survey of evolvable system may lie in determination of its IPB, depending on determining parameters, such as quantity and quality of information coming into the system as well as speed rate of its organization. Such survey is aimed at the description of all possible bifurcations, plotting of a range of bifurcation set at a range with various type of phase portraits and to indicate a phase portrait corresponding to every range with IPB domain. Using the words of great I.P. Pavlov “all types of life, from the simplest to the most complex organisms, including human, is a long line of ever complicating to the highest degree equilibriums of the external environment”. It appears that these words can best characterize the perspective applications of the CS analysis presented herein.


sensitivity; multifractal structure; mechanical properties; dimension; boundary of information perception; information


Haken H. Synergetic Computer and Condition. 2ͩ enlarged edition. Berlin: Springer, 2004, 244 p.

Pask G. and Lerner A.Ya. Model' evolyutsii [Model of evolution]. Principy samoorganizacii [The principles of self-organization]. Moscow, 1966, рр. 284-314. Available at: (in Russian).

Foerster H.A and Pask G. Predictive Model for Self-Organizing Systems. 1961, pp. 258–300.

Dubrov Yu.I. Lyudina v suchasnomu virobnitstvi: problemi psihichnoyi stiykosti ta intelektualnoyi mobilnosti [Man in modern production: problems of mental stability and intellectual mobility]. Visnyk Natsional’noi akademii nauk Ukrayiny [Bulletin of the National Academy of Sciences of Ukraine]. 1998, no. 4, pp. 81–90. (in Ukrainian).

Eigen M. and Schuster P. The Hypercycle. A Principle of Natural Self-Organisation. Part B: The Abstract Hypercycle. The Science of Nature = Naturwissenschaften. 1978, vol. 65, iss. 1, pp. 7–41. Available at:

Eigen M. and Schuster P. The Hypercycle. A principle of natural self-organisation. Part C: The realistic hypercycle. Science of Nature. Naturwissenschaften. 1978, vol. 65, iss. 7, pp. 341–369. Available at:

Sharl G., Benne P. and Landaujer R Fizicheskiye predely vychisleniy [Physical limits of computing]. V mire nauki [In the world of science]. Scientific American. 1985, no. 9, рр. 24-37. Available at: CALC/CALC.HTM (in Russian).

Volterra V. and Gabay J. Lecóns sur la théorie mathematique de la lutte pour la vie. Paris: Gauthiers-Villars, 1931, 214 р. Available at:

Lotka A.J. Elements of Physical Biology. Baltimor: Williams and Wilrins company, 1925, 495 p. Available at:

Solbrig O. and Solbrig J. Introduction to Popular Biology and Evolution. USA: Addison-Wesley, 1979, 468 р. Available at:

Frolov Yu.P. Pavlov i ego ucheniye ob uslovnykh refleksakh [I.P. Pavlov and his theory of conditioned reflexes]. Moscow, Leningrad: Gos. izd-vo biol. i medits. lit-ry, 1936, 250 р. Available at: (in Russian).

GOST Style Citations

Haken H. Synergetic Computer and Condition. A Top-Down Approach to Neural Nets / H. Haken. - 2ͩ enlarged edition. - Berlin : Springer, 2004. - 244 p.


Паск Г. Модель эволюции / Г. Паск // Принципы самоорганизации : сб. докл. : пер. с англ. / под ред. и с предисл. А. Я. Лернера. - Москва, 1966. - С. 284-314. - Режим доступа:


Foerster Н. V. Part I : Cybernetica 3 // Pask G. A Predictive Model for Self-Organizing Systems / G. Pask, Н. V. Foerster. - [Urbana], 1961. - P. 258–300.


Дубров Ю. Людина в сучасному виробництві: проблеми психічної стійкості та інтелектуальної мобільності / Ю. Дубров // Вісник Національної академії наук України. - 1998. - № 4. - С. 81-90.


Eigen M. The Hypercycle. A principle of natural self-organisation. Part B: The abstract hypercycle / M. Eigen, P. Schuster // The Science of Nature = Naturwissenschaften. - 1978. - Vol. 65, iss. 1. - P. 7–41. - Available at:


Eigen M. The Hypercycle. A principle of natural self-organisation. Part C: The realistic hypercycle / M. Eigen, P. Schuster // The Science of Nature = Naturwissenschaften. - 1978. - Vol. 65, iss. 7. - P.  341–369. - Available at:


Шарль Г. Физические пределы вычислений / Г. Шарль, П. Бенне, Р. Ландауэр // В мире науки = Scientific American. - 1985. - № 9. - С. 24-37. - Режим доступа: CALC/CALC.HTM.


Volterra V. Lecóns sur la théorie mathematique de la lutte pour la vie / V. Volterra ; еd. J. Gabay. - Paris : Gauthiers-Villars, 1931. - 214 р. - Режим доступа:


Lotka A. J. Elements of Physical Biology / A. J. Lotka. – Baltimorе : Williams and Wilrins company, 1925. - 495 p. - Режим доступа:


Solbrig O. Introduction to Popular Biology and Evolution / O. Solbrig, J. Solbrig. - USA : Addison-Wesley, 1979. - 468  р. - Режим доступа:


Фролов Ю. П. И. П. Павлов и его учение об условных рефлексах / Ю. П. Фролов. – Москва ; Ленинград : Гос. изд-во биол. и медиц. лит-ры, 1936. – 250 с. - Режим доступа:


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