A.A. Khadartsev, professor, Dr.Med.
Tula state university, Tula
A.A. Nesmeyanov, professor, Dr.Med.
Nordmed ltd., St.Petersburg
V.M. Es’kov, professor, Dr.Biol., Dr.Sc. (Phys.-Math.)
Surgut state university, Surgut
N.A. Fudin, professor, Dr.Biol.
P.K. Anokhin Research institute of normal physiology, Moscow
A.A. Kozhemov, Ph.D.
Kabardino-Balkarian state university, Nalchik

Key words: sport, basketball, piterbasket, synergetics, chaos theory and self-organization, quasiattractors.

Introduction. In any sport elementary training of an athlete is associated with a specific algorithm of phased learning of the theory: history of sport, principal achievements in it, physiological characteristics of different systems (blood circulation, respiratory, locomotor etc.) and technique inherent in selected kind of sport. It is also assumed to use a stage-by-stage system of control for the acquired theoretical and practical skills.

Effectiveness of learning can be provided in case of available natural qualities and body characteristics: power, speed, endurance, having a genetic predetermination. These hereditary properties are chaotic and their further development or lack of development depends on external control actions of learning and training. They are caused by the degree of interaction and inter-assistance of a trainer and an athlete, are based on the scientific approach to the intensity and duration of physical training loads, development of coordination, locomotor function, and involve regulation of metabolism, depending on the nature of loads. The psychological component in pre-season and season training is equally important, which is based on the regular basic psychological training, that forms the steady motivation to win, cope with the lack of self-confidence, be able to focus mentally on the right time, cope with fears of famous athletes in competitions.

In this paper V.F. Gorbatyuk [5] presents the model of learning physics and mathematics and natural sciences on the basis of synergetics. It identifies the opportunities for the constructive role of chaos in self-organizing systems, a model of learning and self-learning of teachers is proposed on the basis of the cyclic model with a certain order of acquiring and applying knowledge. The artificial chaos is created in study groups, contributing to the emergence of self-learning and mutual learning groups. But it is good when considering a certain theoretical subject.

Originally there is chaos in athletes’ training (uncertainty of physical and psychological conditions, physiological statuses). It seems inappropriate to introduce additional elements of chaos. It is required to correct the orientation of the athlete’s body state vector using external control actions (dynamic exercises, psychological trainings, training techniques, etc.). The order parameters can be determined using the developed and patent-protected programs. These programs represent the practical implementation of the main provisions of the chaos and self-organization theory (CST) [8, 10, 11 et al.].

In the 80-s of the last century the science synergetics arose, studying joint cooperative actions in systems and combining by the general laws different sciences: physics, chemistry, biology, psychology, philosophy, etc. In particular, synergetics first formulated the universal laws of evolution, just both for physical (fusty) and biological (living) world and society. It is replaced by the CST.

The synergetic pedagogics of sport, as a system of trainer and athlete interaction, provides the effect of the new qualitative improvement of collective’s creativity aimed at implementing the new goal of training staff to get a creative side product with the help of students. New means of the computer environment optimize communication and development of the information product. Such a pedagogics uses new methods of data processing to implement training [4] and accumulates the knowledge regarding the peculiarities of the operation of functional systems of the human body. Trainer and athlete’s activities are forms of creativity. A trainer has to deal with the material "object" - a biological object, which must be transformed in accordance with the set purpose (achievement of specific result). But a compulsory condition is functional systems in collaboration with students, that have chaotic variability and may provide an unexpected result.

There is enough evidence that synergetics is the third global paradigm (historically: the first - deterministic, the second - stochastic). Underestimation of this fact by scientists, the whole intellectual community hampers the dynamic development of sport and humanity in general. In science, there are complete certainty (within the deterministic paradigm), partial uncertainty (within the stochastic paradigm) and total uncertainty (within the synergetic paradigm). In view of the synergetic analysis the physiological basis of visual perception in training of athletes confirms one of the basic principles of existence of complex human systems, which is self-organization. This phenomenon is common to athletes, providing maximum achievements, records. The human body has self-organizing physiological systems at various levels, including at the level of the brain, providing the visual perception of harmonic motions in training and competitive periods and laying the base for the implementation of educational ideas, receiving a powerful tool to achieve their goals. The contingency of functions of the human body and the functional activity of the brain, stipulating for specific features of man’s locomotor (musculo-skeletal) system, the manner of aesthetic perception of the world with the visual apparatus should be taken into account when teaching different sports, when irrelevant to people parts can, as a joker, dramatically change the nature of athlete’s training.

Every great athlete is different, and his technique is sometimes very different from the generally accepted and deterministically caused one. It is this individuality that is an example of organized chaos, initiated by physiological make-up (but not constants) of an athlete’s body.

The purpose of the study was to give a scientific substantiation of the use of the sports game piterbasket as a rehabilitation technology in terms of the chaos and self-organization theory.

Materials and methods. The new method of identification of matrices of inter-attractor distances was suggested, ensuring assessment of the influence of physical load on the human body [10 et al.]. The method is used for group comparisons (different groups of people, different types of impacts, different types of therapeutic measures, physical loads or sports), when there are several data clusters (for each group surveyed or for each type of impact on the group of subjects) and these clusters are described by their vector of human's body state (VHBS). The integrative measure of effectiveness of therapeutic or sports effect is the degree of similarity (or, conversely, remoteness) of these two compared quasiattractors in the phase state space (PSS). In addition, each person with his own set of features (components of VHBS) is set by a point in the PSS, so the group of subjects forms a "cloud” (quasiattractor) in PSS, and different groups (due to different effects on them) form different "clouds” - quasiattractors in PSS. Distances Zij - (here i and j – numbers of groups surveyed) between the chaotic centers of these different quasiattractors form the matrix Z, which define all possible distances between their chaotic centers, describing the state of different groups of subjects prior to the impact of exercise and after an exposure. Moreover, the maximum differences in distance between the chaotic centers of quasiattractors Zij of the motion of VHBS of different groups of subjects (before and after a specific load) corresponds to the maximum efficiency of sports event, and their reduction requires further adjustment of the impact load [7, 10].

As a part of the present work researches of groups of students of Surgut and Samara universities (young men and women) with different levels of physical fitness were carried out. Group 1 - students engaged in team sport (football, volleyball, basketball); group 2 - students engaged in individual sport (weightlifting, power lifting); control group 3 - students engaged in physical education (PE) occasionally, but only twice a week as a part of the state program on PE. Young women surveyed were conventionally divided into two groups: group 4 - female students engaged in team sports (football, volleyball, basketball); comparison group 5 - female students engaged in PE occasionally (twice a week as a part of the state program on PE). A similar division was made for Samara students. The indicators of autonomic nervous system (ANS) (Tab. 1-4) are the coordinates of VHBS (x₀= SYM - sympathetic, x₁ = PAR - parasympathetic, x₂- BSI – Baevsky’s stress index, x₃ – SPO₂ - oxyhemoglobin saturation in the blood of subjects (%), x₄- pulse).

In addition, subjects’ involuntary limb movements (tremorogram) were recorded using patented devices and the quasiattractors of motion of SSV (system state vector) in the two-dimensional phase space of the vector x=(x₁,x₂) were calculated based on the obtained amplitude-frequency responses (AFR) of tremorograms in the coordinates x₁ – limb displacement, x₂=dx₁/dt - displacement velocity. The value of Shannon entropy for the tremor and the value of Kullback-Leibler divergence were calculated [3].

Development of the methods of the chaos and self-organization theory - CST in the study of actions of any physiological functions of the human body has underlay the creation of new software products, devices and models in the area of CST [6 et al.]. The data were processed using a special patented program and the method that provided by the received frequency characteristics, cinematograms and derived values ​​of velocities (after a signal differentiation) the design of phase planes (coordinates x₁ and x₂ = dx₁/dt), as well as the definition of the limit of motion of the vector of the state of hand (during tremor) in this PSS and evaluation of the dimension of the quasiattractor of PSS, within which the vector moves.

Simultaneously, the compartmental-cluster modeling of these processes was performed [2, 8]. Initially, two approaches in the models are possible: models in the single cluster (effector) level, for example in the form of three compartmental systems, and hierarchical models. It is essential that such a hierarchical system does not represent direct control [2]. The studies contain the results of modelling within single cluster, three compartmental models. The models of V.A. Antonets describing the operation of neuromotor compositions consisting of three blocks (compartments) [1] were used in the stochastic approach.

Results and discussion. Proceeding from the analysis of matrices of Zij interattractor distances between chaotic centers of quasiattractors of VHBS of trained and untrained young men and women of Surgut before and after a load in the 5-dimensional phase space in comparison with the representatives of Samara, the shortest interattractor distance Z₃₂= 3,23 c.u. is obtained when comparing the 3rd and the 5th groups of young men and women respectively, and the highest - in the comparison of female athletes of the 4th group and young men of the 2nd group and comprises Z₂₁= 41,10 c.u. In this comparison the gender differentiation is less significant than the applied load that is reflected in Tab. 1.

The analysis of matrices of interattractor distances during gender differentiation after a load shows the longest interattractor distance Z₁₂= 444,05 c.u. when young women from the 5th group are compared with young men from the 1^st group of observations and the shortest distance Z₃₁= 22,07 c.u. when the 4th group of young women is compared with young men from the 3^rd group. xi was represented by: x₀ - SYM, x₁ - PAR, x₂ - BSI - all in c.u., x₃ - SPO₂ - oxyhemoglobin saturation in the blood of subjects (%), x₄ - HR - heart rate (bpm).

Table 1. Matrices for identification of Zij distances between chaotic centers of quasiattractors of the body state vector of trained (1^st and 2^nd groups of young men and 4^th group of young women) and untrained (3^rd group of young men and 5^th group of young women) students of Surgut before exercise in the 5-dimensional phase space

Analyzing the Zij distance matrices between chaotic centers of quasiattractors of VHBS of trained and untrained young men and women from Samara before the load in the 5-dimensional phase space, Z₃₂= 2,56 c.u. was the smallest when comparing the 3^rd and the 5^th groups of young men and women, respectively (which is also noted in a similar comparison in Surgut). When comparing the 1^st and 4^th groups Z₁₁= 2,33, and the highest - in the comparison of young female athletes of the 5^th group and young men of the 2^nd group, which comprises Z₂₂ = 39,03 c.u. (Tab. 3).

Table 2. Matrices for identification of Z_ij distances between chaotic centers of quasiattractors of the body state vector of trained (1^st and 2^nd groups of young men and 4th group of young women) and untrained (3^rd group of young men and 5^th group of young women) students of Samara before exercise in the 5-dimensional phase space

Table 3. Matrices for identification of Zij distances between chaotic centers of quasiattractors of the body state vector of trained (1^st and 2^nd groups of young men and 4^th group of young women) and untrained (3^rd group of young men and 5^th group of young women) students of Surgut before exercise in the 5-dimensional phase space

Table 4. Matrices for identification of Zij distances between chaotic centers of quasiattractors of the body state vector of trained (1^st and 2^nd groups of young men and 4^th group of young women) and untrained (3^rd group of young men and 5^th group of young women) students of Samara after exercise in the 5-dimensional phase space

One of the major problems of organization and control of tremor parameters related to the level (degree) of chaotic behavior of the studied processes. In other words, voluntary or involuntary movements underlie postural tremor. However, this problem is related to broader theoretical assumptions and concerns the global problem of the role of chaos in the life support of special animal and human organisms in particular.

The information on improvement of physical and mental abilities of primary schoolchildren in the conditions of application of the modified game piterbasket is specified in [12].

Researches of the accented application of affecting play environment (piterbasket) on physical education lessons, extended in 2009 in the early grades of school № 3 in Nalchik, using the parallel-group studies, have confirmed the positive impact of classes according to the author's methodology on the quality of integrated development of children’s physical and mental abilities.

Primary schoolchildren were divided into experimental and control groups (2, 3 and 4^th formers). In the control groups lessons were conducted in accordance with the current program, recommended by the Ministry of Education and Science of the Russian Federation for the use in school educational institutions (A.P. Matveev, T.P. Petrova, 2002). In the experimental groups physical education lessons were conducted in compliance with the basic program with the inclusion of the second half of the active game piterbasket to the main part of the lesson.

The proposed methodology is notable for the opportunity to use the active game piterbasket along with the performance of the compulsory minimum content of education, without increasing the academic hours devoted to physical education classes. Better progress in basic subjects (Tab. 5) in the experimental classes compared with control ones due to the acquisition of skills to quickly switch from one type of motor activity to another, increasing attention concentration, thinking, intelligence, mental structures, formed in primary pupils (7-10 year olds), internal position defining the attitude to school and peers. The developed and tested experimental methodology has led to the formation in children of the appropriate type of leading activity (according to Vygotsky’s classification, 1983).

These results confirm the well-known statement: "Full working practice can be formed only on the basis of play and learning ones, and learning activity only on the basis of play one, because the aim of teaching is, in particular, mastery of such abstractions and generalizations, which suggest the presence of imagination and symbolic function in a primary schoolchild, which are developed in a game" (V.V. Davydov). Along with changes in the subjects’ autonomic status (for the increase of sympathicotonia) we observed changes in progress in studies (Tab. 5).

Table 5. Progress indicators of 2-4-fomers in basic subjects, X±m

It can be stated that in a game a primary schoolchild has freedom of choice of play behavior, which provides a "zone of proximal development", affects the formation of not only intelligence, but also an integral “self” as the basis of personality development.

Analyzing the overall findings, we can conclude that the application of the developed methodology using a modified game piterbasket not only helps to improve the educational process on the subject of "Physical Education" in 1-4 classes, but also stimulates the teaching cognitive sphere of children in general [19]. It is shown in the changes in parameters of quasiattractors of VHBS, which have a dynamics of changes similar to those in Tables 2-4. Increased motivation affects the parameters of tremorograms that will be presented in our subsequent message.

Conclusion. The use of physical exercises in the form of game competition (piterbasket classes) and improves the athletes' sensomotor activity. Visual orientation, permanent monitoring of moving objects, selection of time and forms of performance in the play situation activate the mechanisms of the visual-motor coordination. The influence is particularly clear in the "eye-hand" system. Turns and rotations contribute to improvement of the mechanisms of vestibular tolerance. Action with a ball – catching, passing and throwing it to the basket - increase tactile and kinesthetic sensitivity and develop more subtle muscle differentiations of applied efforts. The special value of this type of play activity is to improve responsiveness and speed of actions, involving acceleration compared with the usual norm of processes of analysis and synthesis, being implemented in the higher parts of the brain.

Such a dynamics of development of organizational processes during any training session (and especially in piterbasket) was confirmed by the method of identification of matrices of interattractor distances. The participation in piterbasket competitions results in a complex impact on the improvement of motor and psychomotor functions of the body, including emotional and intellectual spheres. Interpersonal communication is being expanded. This play form of exercises with a ball has an effective therapeutic potential, which can be used in the range of means of psychophysical rehabilitation.

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Author’s contacts: apokin_vv@mail.ru