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The influence of industrial low-frequency electromagnetic fields on the human body is currently insufficiently studied. However, such fields are quite common in modern automated production, where various electric drives are used, and they significantly affect the quality of human life. This is especially evident in the conditions of the North, where special ecological factors cause significant changes in the systems of regulation of the body's functions. This study examines the influence of such fields on the parameters of the cardiovascular system of female workers in the oil and gas industry in Russia. Four groups of women were studied, differing in age and electromagnetic field exposure. As a result, the effects of influence of the fields were revealed, especially for the older age group.

Fifteen matrices of paired comparisons of tremorogram samples were constructed using a tremorograph. The number k of pairs with Wilcoxon’s test p ≥ 0.05 was very small, which was indicative of a lack of statistical robustness of the samples.

One of the main problems in the theory of homeostasis and the theory of functional systems of the human body is the problem of choosing standards. It turned out that the statistics poorly diagnose the norm (standard) of function of the human body. The aim of the study was to assess the possibility of using a new quantitative criteria - the area of the pseudoattractors (Eskov's quasiattractors) as standard (physiological norm) parameters. Methods. In a group of 15 women (mean age = 28 ± 2,3 years, who have been living in the North of the Russian Federation in Ugra for more than 15 years), cardiointerval samples were recorded (300 cardiointervals per sample) 225 times for each test subject. As a result, we calculated 15 matrices of pairwise comparisons of samples. A total of 225 matrices for all 15 subjects and 225 areas of S pseudoattractors for each subject were created. Area S was found from the formula S = Δx1 х Δх2, where Ax1 is the range for cardio intervals, and Δx2 is the range for Δx1. Results. All 225 matrices for 15 subjects showed showed a substantial variability in samples of cardiointervals. However, S areas showed statistical stability for each of 15 subjects. Conclusions: further application of statistics in the calculation of cardio intervals is problematic due to the statistical instability of the samples, therefore we propose to use areas of pseudoattractors to assess the physiological norm.

Over the past 100-150 years, the selection of homogeneous groups in ecology as a whole has been carried out as part of the calculation of the coefficient of variation V = о / or by the ABC method. However, the Eskov - Zinchenko effect imposes serious restrictions on all statistical methods. The aim of the study was to verify the statistical homogeneity of three groups of Khanty women of different ages. Methods: The technique of repeating measurements of the same parameters of the Khanty women's cardiovascular system (three different ages) was used, for which matrices of all (105) different pairwise comparisons of samples for each such group were constructed (these measurements were repeated). Results. It was established that the same age, gender and living conditions (ethnicity) do not guarantee the selection of physiologically (statistically) homogeneous groups of subjects. The study proves the lack of statistical homogeneity of the three age-tested groups of Khanty women. The proportion of statistical similarity is less than 20 % of all 105 comparison pairs in all three age comparison groups. It is shown that repeated measurement of the same group gives a different picture of the distribution of pairs that can be attributed to one (common) general population. Each new dimension will give other pairs of k coincidences and it will never (from the standpoint of stochastics) be able to select a homogeneous group statistically coincident in the xi samples of the homeostasis parameter. In fact, the Eskov - Zinchenko effect spreads from one subject (in the mode of n iterations of experiments) to a group of different subjects (which cannot be homogeneous). Conclusions. From the standpoint of chaos theory - self-organization, other criteria of group homogeneity are required, in which the parameters of quasi attractors and the ratio of objects of these quasi attractors are already calculated.

The study examined stochastic stability of EEG samples recorded in succession from the same healthy volunteer at unchanged state. The absence of statistical repetitions not only for EEG samples, but also for the corresponding spectral densities was proven. A method to calculate the pairwise comparison matrices of ECG samples and quasi-attractors was proposed. The diagnostic effectiveness of these calculations was demonstrated during photostimulation, when successive EEG samples chaotically changed under overall homeostatic conditions.

The founder of the homeostasis theory W. B. Cannon spoke about the lack of stability of homeostasis and systems of homeostatic regulation. However, to date, the postulate of the statistical stability of samples of homeostasis parameters in various functional systems has been working in human ecology. The aim of the study is to verify this fundamental postulate and to prove the lack of statistical stability of samples of the neuromuscular and cardiovascular systems. Methods: age-related dynamics of cardio intervals was studied in three groups (38 people in each group) of Khanty women and three groups of newcomers (228 people in total), tremor and tapping parameters were studied in two groups: women (18 people) and men (16 people). The Elox-01 device was used to record cardio intervals, and the patented tremograph was used to record tremorograms. Results: the absence of statistical stability of tremorograms was proved (the number of samples of k pairs that have one sampled population not more than k1 < 5 % for tremor and k2 < 12 % for tapping), for cardio intervals k3 < 17 %. The samples are not homogeneous, the probability of their statistical repeating in a row is p < 0.05 (for one subject in constant homeostasis). It is proposed to calculate the parameters of quasi attractors that really demonstrate statistical stability (in constant homeostasis). Conclusion: the samples of the parameters of neuromuscular and cardiovascular systems are not statistically homogeneous (they change chaotically). In this regard, to assess the norm (standard) of homeostasis, it is advisable to use the calculation of the parameters of quasi attractors along the first coordinate x1 (for example, the parameters of cardio intervals or tremorograms) and x2 (rate of change x1).

Despite ever wider use of neural computers (NC) and their simulators − neural emulators − in medicine, their further use comes up against the fundamental impossibility of using them to solve tasks of systemic synthesis (finding the most important diagnostic signs, $$ {x}_i^{\ast } $$ , in medicine). This article presents two new principles (the chaotic organization of the initial state of weightings Wi0 of xi features and the principle of multiple reverberations), which can be solved using NC for systemic synthesis. Examples of the use of such special operating modes in cardiovascular physiology are presented. Uncertainties of types 1 and 2 in medicine are considered; these cannot be resolved within the framework of stochastics.

This paper presents two new fundamental principles of the functioning of real neural networks of the brain. These principles have inspired the design of artificial neural networks (a neuro-computer). In addition to well-known properties of artificial neurons (threshold properties, neural network formation, and backward propagation of errors), we describe two new major properties of real neural networks of the brain by which a neuroemulator may work. We discuss the practical usefulness of these properties for the neuro-computer. The first property is permanent statistical chaos in the structure and functions of the brain neural networks. The second property is reverberations, or multiple iterations, in the work of neural networks. The introduction of these two properties to the work of the common artificial neural network provides a new quality, that is, solving the problem of systemic synthesis and finding rank parameters. Modern science has not investigated and solved this problem, which is a general fundamental problem in medicine. It has been shown that this task is identical to the heuristic activity of the brain.

Analysis of North environmental factors and they influence on human body have special problem according to absent of statistic stability of any samples parameters. Now it is known as Eskov-Zinchenko effect and the effect needs new theory and new methods for description of specific behavior of biosystems. So we presented the Eskov-Zinchenko effect and new methods of system synthesis. The last method is based on investigation of order parameters and calculation of a special model for cardiointervals aging dynamic and its descriptions.

The problem of studying the effects of climatic-ecological factors of territories to the formation of specific conditions of the human environment and human health in general is very relevant. The study of influence of such factors on the functional state of the body, it is expedient to study within the framework of the new theory of chaos-self-organization (there are a number of fundamental differences from the tacit stochastic approach). In this regard, we set the aim: consider and forecast in individual and groups the characteristics of the state of the neuromuscular system of a person living in the territory of the Khanty-Mansiysk Autonomous Okrug - Yugra from the standpoint of chaotic dynamics of electromyograms parameters. New methods of data visualization were used (obtaining phase portraits EMG in coordinates x(t) - muscle biopotentials, and x2 = dx/dt - the rate of their change) recorded using an electromyograph, a time scan of the signal was constructed, which was converted by sampling the signal into some numerical series and for them the parameters of quasi-tractors were calculated. Results. In the work, multiple measurements of the parameters of the bioelectrical activity of the muscle were analyzed from the position of the Eskova-Zinchenko effect, i. e. with repeated (identical) experiments before and after a local cold exposure in a group of girls. Analysis of the obtained time series showed that the signal is always unique for each recording interval for each subject. Cooling of the limb leads to an increase in the size of quasi-tractors, which is difficult to document in the framework of statistics (there is a continuous statistical change in electromyograms). Conclusions. The practical possibility of applying the method of multidimensional phase spaces (calculation of quasi-tractors parameters) for identifying real changes in the parameters of the human neuromuscular system in conditions of cold stress is proved. Calculation of the parameters of quasi-tractors is necessary as a quantitative measure of the reaction of the organism to external influences.

Arbitrary and involuntary movements were studied from the position of the new chaos-self-organization theory. Analysis of organization of tappingrams and tremorograms within the framework of N. A. Bernstein "repetition without repetitions" hypothesis leads to the Eskov-Zinchenko effect. In this case, there is no statistical stability for samples of parameters of electromyograms of any movements obtained in a row, i.e. fj (xi)≠fj+1(xi) with the probability p≥0.97. In this paper, the basic problem of motion physiology, stochastic instability establishment mechanisms, is solved in the analysis of muscle electromyogram parameters under conditions of permanent static force. Statistical instability of electromyograms within the framework of the Eskov-Zinchenko effect is proven.

The problem of the existence and special properties of third type systems has been formulated within the new chaos–self-organization theory. In fact, a global problem of the possibility of the existence of steady-state regimes for homeostatic systems has been considered. These systems include not only medical and biological systems, but also the dynamics of meteorological parameters, as well as the ambient parameters of the environment in which humans are located. The new approach has been used to give a new definition for homeostatic systems (complexity).

The evolution rate v(t) varies among diverse biosystems, but a general theory can be formulated when the dynamics of the biosystem stater x = x(t) = (x1, x2, x m ) T is considered in the m-dimensional space of states. A mathematical approach is proposed for evaluating such processes and describes the processes in terms of particular chaos of the statistical distribution functions f(x). In the case of complex multicomponent systems with a high dimension number m (m ≫1) of the phase space of states, we propose using pairwise comparison matrices of samples x(t) when homeostasis is constant and calculating the parameters of quasiattractors. The Glensdorff–Prigogine thermodynamic approach to estimating evolution is inefficient in assessing the third-type systems, while it is applicable and the Prigogine theorem works at the level of molecular systems. Alterations in the state of the human neuromuscular system were found to lead to chaotic changes in the statistical functions f(x) in tremor recording samples, while quasiattractor parameters demonstrate a certain regularity.

Homeostasis is a basic concept in investigating all living systems. Homeostasis and life are synonyms to a certain extent. The concept of homeostasis has been studied and developed for more than 150 years; however, only the 21st century brought us close to understanding homeostasis as a state of a biosystem and a continuous process. The chaos and self-organization theory (CSOT) proves that the conventional views based on determinism (functional analysis) or stochastics (when stochastic uncertainty or certainty occurs) cannot describe homeostasis as defined by W.B. Cannon and his followers. The new CSOT shows a clear boundary between determinism, stochastics (and deterministic chaos), and third-type systems, which have five special properties (principles of self-organization) and can be described in terms of quasiattractors. Kinematics is understood as the motion of quasi-attractors in the phase spaces of states. Complexity is introduced as the rate of evolution of complex biological systems, differing from the definition by Prigogine–Glansdorff. At the same time, concepts of uncertainty of the first and second types and an analog of the Heisenberg calculus are introduced for complexity. According to these concepts, complex biosystems are transferred from the area of traditional science to a new area of the theory of chaos and self-organization.

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).

The necessity of studying the Bernstein effect "repetition without repetition" is dictated by the absence of quantitative description of this effect and models that could describe such unique phenomena as repeated limb movements in a person in various mental states. In 30 nominally healthy volunteers (15 men, 15 women aged 24-25 years), tappingrams and tremorograms were recorded using an eddy current sensor with an oscillatory circuit (1 MHz) and an amplifier with recording frequency 0-1000 Hz and minimum amplitude of 0.01 mm. The results were recorded as files, processed as matrices of paired comparisons of samples, the number of matching sample pairs was determined (significance level p>0.05), and phase trajectories of finger movement were plotted. The effect was observed for both tapping and tremor and it is advisable to calculate the parameters of quasi-attractors that changed upon shifts in homeostasis.

The founder of information theory W. Weaver in 1948 and the theory of “Fuzziness” L.A. Zadeh spoke about the specifics of the behavior of living systems. In particular, W. Weaver took all living systems-systems of the third type-beyond the stochastic and deterministic approaches. Over the past many decades, no one has tried to test the hypotheses of these scientists from the standpoint of a special information approach to the description of biosystems. In recent years, the Eskov-Zinchenko effect was discovered, which dramatically changed the methods in the description of living systems. This effect is based on the proof of statistical instability of the samples of parameters of any functions of the human body. In this case, an analog of the Heisenberg uncertainty principle is introduced in the description of biosystems. As a result, new information technologies and new models for describing biological systems are emerging.

The problem of life expectancy of indigenous and non-indigenous population of northern territories of the Russian Federation is considered in terms of economic growth and industrial development of the northern territories. The importance of prolonging the period of active working age of non-indigenous population of Khanty-Mansi Autonomous Okrug-Ugra and Yamalo-Nenets Autonomous Okrug is increasing. Four directions for possible prolongation of the active life of non-indigenous population were presented. The problem of comparative dynamics of age-related changes of cardiovascular system on three specific age groups of female indigenous and non-indigenous population is being considered. A decrease in volume of quasi-attractors in the phase space of states is equivalent to strengthening of physical activity, which is typical of normal aging. It is proposed to use the mathematical pattern to reduce these volumes in assessing the dynamics of human aging in the North.

Human-scaled (in complexity) systems possess a unique feature, viz., the continuous random motion of many components of the state vector x = x(t) of such living systems. Taking this property into consideration causes the rejection of any of the known types of stationary modes (e.g., dx/dt = 0) and requires revision of the concept of chaos. A new approach to the understanding of living systems (as a third paradigm of the natural sciences) and new methods for the study of living systems (as a theory of chaos and self-organization) are proposed. Common grounds of physics and theory of chaos and self-organization are revealed as a generalized uncertainty principle and a limit on the parameters of quasi-attractors.

The fallacy of using a neuroemulator only once or with a small number of iterations (p ≤ 50) to solve the group-separation problem (a binary classification problem) in a five-dimensional phase space has been demonstrated using the example of the parameters of five active components (of the 14 that were registered) of the state vector of the cardiorespiratory system in Khanty (indigenous people of Yugra, Russia) women from three age groups. The necessity of repeating the neuroemulator-based solution of the binary classification problem at least 1000 times has been demonstrated: in this case, the most significant diagnostic features, xi, could be identified with a precision of two significant fraction digits that are most relevant for the diagnostics of the aging rate (finding a solution of the system-synthesis problem in gerontology).

It is proposed to construct the kinematics of complex systems (systems of the third type) based on simulation of the motion of the state vector of the system x(t) in the phase space of states. A new concept of stationary modes of these systems, which is different from the analog in mechanics (when dx/dt = 0) and statistical interpretation (when the distribution function f(x) does not change significantly), is introduced. For systems of the third type, dx/dt ≠ 0 is always met and f(x) for all consecutive samples (e.g., cardiointervals) varies continuously. A unit for calculation of the motion of centers of quasi-attractors (QA, regions of phase space, where x(t) changes continuously) is presented. The concepts of velocity and acceleration of evolution are introduced. The concepts of uncertainty of the first and second kinds are given. Examples of rectilinear and curvilinear motion of x(t) in the phase space (from gerontology for groups of women of different ages) are given.

Investigation of distinctions discovered between three groups of different age female-khanty (indigenous population of Ugra, Russia) of five active components (from all 14 components registered) of a state vector of cardiovascular system shows the wrong solving binary classification problem in a five dimensional phase space by one iteration or a few iterations p (p≤50) using a neuroemulator. We prove that solving binary classification problem by a neuroemulator must be repeated about 1 000 times since it provides identifying more significant diagnostic signs хi between two significant figures after comma which exhibit the significance in diagnostics of aging rate (this is system synthesis problem solving in gerontology).На основе изучения различий между тремя возрастными группами женщин-ханты (коренное население Югры, Россия) по параметрам пяти активных компонентов (из всех 14 регистрируемых) вектора состояния кардиореспираторной системы организма продемонстрирована ошибочность (разовой или с малым числом итераций, p≤50) решения задачи разделения групп в таком пятимерном фазовом пространстве с помощью нейроэмулятора (задача бинарной классификации). Доказано, что решение задачи бинарной классификации с помощью нейроэмулятора должно повторяться не менее 1 000 раз, что обеспечит выделение наиболее значимых диагностических признаков хi в пределах двух значащих цифр после запятой, которые демонстрируют наибольшую значимость при диагностике скорости старения (это решение задачи системного синтеза в геронтологии).

The problem of life expectancy of indigenous and non-indigenous population of northern territories of the Russian Federation is considered in terms of economic growth and industrial development of the northern territories. The importance of prolonging the period of active working age of non-indigenous population of Khanty-Mansi Autonomous Okrug-Ugra and Yamalo-Nenets Autonomous Okrug is increasing. Four directions for possible prolongation of the active life of non-indigenous population were presented. The problem of comparative dynamics of age-related changes of cardiovascular system on three specific age groups of female indigenous and non-indigenous population is being considered. A decrease in volume of quasi-attractors in the phase space of states is equivalent to strengthening of physical activity, which is typical of normal aging. It is proposed to use the mathematical pattern to reduce these volumes in assessing the dynamics of human aging in the North.Проблема продолжительности жизни коренного и пришлого населения северных территорий РФ рассмотрена в аспекте нарастания экономико-промышленного освоения этих территорий. Нарастает и значимость пролонгации периода активного трудоспособного возраста у пришлого населения Югры и ЯНАО. Представлено четыре направления возможного продления периода активной жизни пришлого населения. На конкретных трёх возрастных группах женского коренного и пришлого населения рассмотрена проблема сравнительного возрастного изменения динамики сердечно-сосудистой системы. В фазовом пространстве состояний уменьшение объёмов квазиаттракторов эквивалентно усилению физической нагрузки, что характерно для нормального старения. Предлагается математическая закономерность уменьшения этих объёмов для использования при оценке динамики старения человека на Севере.

In 1947 M. A. Bernstein proposed a hypothesis about "repetition without repetition" in biomechanics that was confirmed in psychophysiology by the Eskov-Zinchenko effect. This effect can be applied to all parameters (except the parameters of the neuromuscular system) of human body homeostasis. For instance, this instability can be demonstrated for repeated samples of cardiointerval parameters (and other homeostasis parameters) of the human cardiorespiratory system. Within the framework of the new theory of chaos and self-organization, a method is proposed for calculation of matrices of paired comparisons of cardiointerval samples for assessing the physiological status of the human body and changes in homeostasis. Statistical instability of cardiointerval samples and their statistical distribution functions f(x) for successive cardiointerval samples in one subject is proven.

In accordance with the Heisenberg uncertainty principle, a similar dynamics (behavior) for complex biosystems is postulated. Five peculiar properties and thirteen differences of these specific three-type systems (complexity) from traditional deterministic and stochastic systems determine the need for introducing the uncertainty principle for these specific systems. The value of the special boundary volume of the phase space, $$V_{G^{\min } }$$ , (which is considered as quasiattractor) inside of which the state vector of a biosystem moves chaotically and permanently, is the right side of this inequality. The volumes $$V_{G^{\min } }$$ and $$V_{G^{\max } }$$ really represent the peculiar properties of each dynamic biosystem (or each three-type system) as complexity. Particular examples from biomechanics prove the impossibility of using the deterministic or stochastic approach for the description of complexity, and only methods of the new theory of chaos (self-organization) can be useful for the description of complex biosystems. The possibilities of the practical application of this theory in various fields of biology and medicine are also discussed.

The emergence of a third paradigm, the synergistic paradigm, in general systems theory and the relationship between the synergistic and the cybernetic paradigms are considered. A mathematical foundation underlying the application of new methods of identification of the degree of asynergism in biological systems is given. Results of the application of such methods to the study of the dynamic behavior of variations in the human heart rate under conditions of physical load are presented.

We have identified five special properties of biological systems requiring development of new synergistic study methods. We consider the possibility of constructing some quasi-attractors for biosystems in multidimensional phase space and evaluate the properties of the biosystems based on analysis of the parameters of these quasiattractors and using the three postulates of compartmental/cluster theory. We give some biological examples.