Eskov, Valery V

This year marks the 70th anniversary of the publication of the monograph by N.A. Bernshtein "On the construction of movements" and 60 years since the publication of his eighth essay "The urgent problems of the regulation of motor acts". In these works, for the first time, the problem of uncertainty in the organization (and dynamics of behavior) of all systems, which we now designate as homeostatic or systems of the third type, according to W. Weaver's classification, was first raised. This problem was voiced by N.A. Bernstein as the hypothesis of "repetition without repetition", within which it is possible (as suggested by Bernstein) to describe any motor acts. After a detailed study of the various types of motion in biomechanics, we ascertained that modern deterministic-stochastic science has approached its developmental boundary in the study of living systems, since the main thesis about the repeatability and predictability of the state of the biosystem (neuronets of the brain, the human psyche) is violated. We turn to the study of systems that are in a continuous chaotic regime of changes of any parameters x_i of such (unstable) systems. The Eskov-Zinchenko effect, which is a quantitative proof of Bernshtein’s hypothesis of "repetition without repetition", is that the successively obtained samples x_i (in one, unchanged state) demonstrate a kaleidoscope of statistical distribution functions f(x), i.e. f_j(x_i)≠f_j+1(x_i) for two neighboring registered (from one person) registered samples x_i (i.e., for the jth and j+1th). This erases the boundaries between arbitrary and involuntary movements from the standpoint of their objective, statistical evaluation. Statistical instability of any received samples of parameters x_i, which describe homeostatic systems, requires new concepts and new models - models of homeostasis.

Limited applicability of stochastics and comparing it with the new methods of multidimensional phase space were showed. Quantitative measures of the parameters are quasi-attractors for evaluation of chaotic dynamics on the example of the little finger abductor muscle. Method of multidimensional phase space carried out the study and modeling of complex biological objects (complexity). The state of the neuromuscular system is studied in two modes: a weak muscle tension and strong, almost the maximum force. Used quasi-attractors volumes of multidimensional phase spaces, which provide the identification of real changes in the parameters of the functional state with weak muscles (F1=5 daN) and strong (F2=10 daN) static stress. Analysis of the timebase signal x1(t) obtained with myograph, and autocorrelation functions A(t) signal showed their unrepeatability. Comparative analysis of the biomechanical system is made on the basis of registration of quasi-attractor’s volume, as well as on the basis of analysis of the Shannon’s entropy E. Volume of quasi-attractor’s movements x1(t) и x2(t)=dx1/dt at low load is slightly less than similar amounts of displacement of vector (х1, х2)Т  under a heavy load of musculus abductor digiti mini. The values ??of the Shannon entropy under a heavy load are statistically unchanged. Values of the Shannon entropy under heavy load, not statistically vary on the advisability of entropy approach in the assessment of muscular efforts and the impossibility of application of the theorem of Glansdorff—Prigogine (thermodynamics of nonequilibrium systems) in psychophysiological research. Overall, restricting the use of methods of stochastics and the possibility of using the method of multidimensional phase spaces, have been demonstrated in the Eskov—Zinchenko effect.

The discussion of crucial problems of psychophysiology and natural sciences is presented, in general: are there any recurrences of measured values of psycho­physiological parameters (functions) of a person. It is shown that it is impossible to obtain arbitrarily a repetition of samples for tremor and electromyogram (when trying to maintain static muscular tension), statistical distribution function of samples f(x) is continuously changing. This dynamics is typical for tremor (conditionally involuntary movement) and electromyogram when the higher nervous activity of individual oversees the muscular effort. The involuntary movement (tremor) shows the number of coincidence of electromyogram samples (at unrestricted muscular tension) k, which is similar to such in the matrices of pairwise comparisons of tremor samples. Shannon’s entropy in this case does not change significantly.