Faculty of Physics
M.V.Lomonosov Moscow State University
Regular Article

Shannon Entropy in the Research on Stationary Regimes and the Evolution of Complexity

V. M. Eskov$^1$, V. V. Eskov$^1$, Y. V. Vochmina$^1$, D. V. Gorbunov$^1$, L. K. Ilyashenko$^2$

Moscow University Physics Bulletin 2017. 72. N 3. P. 309

  • Article

The questions of the identification of complex biological systems (complexity) as special self-organizing systems or systems of the third type first defined by W. Weaver in 1948 continue to be of interest. No reports on the evaluation of entropy for systems of the third type were found among the publications currently available to the authors. The present study addresses the parameters of muscle biopotentials recorded using surface interference electromyography and presents the results of calculation of the Shannon entropy, autocorrelation functions, and statistical distribution functions for electromyograms of subjects in different physiological states (rest and tension of muscles). The results do not allow for statistically reliable discrimination between the functional states of muscles. However, the data obtained by calculating electromyogram quasiatttractor parameters and matrices of paired comparisons of electromyogram samples (calculation of the number k of “coinciding” pairs among the electromyogram samples) provide an integral characteristic that allows the identification of substantial differences between the state of rest and the different states of functional activity. Modifications and implementation of new methods in combination with the novel methods of the theory of chaos and self-organization are obviously essential. The stochastic approach paradigm is not applicable to systems of the third type due to continuous and chaotic changes of the parameters of the state vector $x(t)$ of an organism or the contrasting constancy of these parameters (in the case of entropy).

Received: 2016 April 13
Approved: 2017 August 23
87.10.-e General theory and mathematical aspects
Rissian citation:
В. М. Еськов, В. В. Еськов, Ю. В. Вохмина, Д. В. Горбунов, Л. К. Иляшенко.
Энтропия Шеннона в изучении стационарных режимов и эволюции complexity.
Вестн. Моск. ун-та. Сер. 3. Физ. Астрон. 2017. № 3. С. 90.
V. M. Eskov$^1$, V. V. Eskov$^1$, Y. V. Vochmina$^1$, D. V. Gorbunov$^1$, L. K. Ilyashenko$^2$
$^1$Chair of biophysics and neurocybernetics, Institue of natural and technical sciences, Surgut state university,
$^2$Federal State Budget Educational Institution of Higher Education « Industrial University of Tyumen», Tyumen, 625000, Russia
Issue 3, 2017

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