The paper proposes the method of determining the membership of the object to chaotic systems on the basis of structural risk minimization. It is presented examples that demonstrate the effectiveness of the methodology to model data. The methodology is based on Chebyshev polynomials that can make an informed choice of uniform distribution law or motivated to prefer a different probability density. The main feature of chaotic systems is the presence of a uniform law of distribution, which is typical for systems of the third type - the foundations of modern theory of chaos and self-organization. It is significant that in the theory of chaos and self-organization at short time intervals τ always be uneven distribution. However, it is impossible to keep the system for a long time in this state.

The paper presents the first attempt to combine methods of stochastics (mathematical statistics) and methods of theory of chaos and self-organization for studying such complex (chaotic) processes as postural tremor. It was established that when re-registering tremor in each subject by n=15 or n=30 obtained tremorograms do not exhibit normal distribution, and non-parametric distributions show distinctions at pairwise comparison on Wilcoxon test (only 2 or 3 pairs from 210 may belong to the same general population). Static physical load sharply changes this picture and the number of such ("similar") pairs increases. The estimation method for effect of a load on tremor is proposed. Simultaneously, within calculating quasi-attractors there is a clear picture of division of chaotic dynamics of tremor parameters with load and without load. Prospects of a new method application in physiological measurements are discussed. Limited method of stochas- tics in description of complexity is underlined, and necessity of calculation quasi-attractor´s parameters in phase space of state is proved.

In the framework of the compartmentae-cluster approach there is possibility of constructing adequate mathematical models that may be of several types supposedly stationary modes of biomechanical systems: in the traditional deterministic approach, when the state vector оf the biomechanical system have equal value and in the framework of the new theory of chaos and self-organization, when system state vector x=x(t)=const. The vector can occur within a bounded volume of the phase space of states. The message signals presented arbitrary human motion under the influence of an alcoholic beverage and the simulated signals for a given external exposure control (Ud=60 у.е.) was compared. Different values ​​of the damping coefficient (b=1,1; b ´= 3,4) present the normal and unnormal state of human body. A comparison was made, the resulting figures and draw conclusions about the impact of damping coefficient on the size of the area of ​​quasi-attractor. Present the state of the biological dynamical system (the human body) under alcohol effect and in normal state.

Transition from determinism to stochastic sand further to chaos (self-organization) in the study of biomechanical systems leads to the problem of chaotic dynamics modeling of a post- ural tremor. In general, there is a problem of identifying the voluntary human movements. In other words biophysics of complex systems has approached the global challenges of voluntary and involuntary performance of any motor functions. The possibility of modeling these processes qualitatively and quantitativelyisdiscussed. Specific models demonstrate the effectiveness of the compartment-cluster modeling of biosystems and possibilities of controlof such models from the neural networks of the brain. Comparative analysis of the simulated and real recorded signals has shown a high consistent dynamics of simulated and real signals of complex biological systems. In particular, changes in tremor parameters can be described by the change in quasi-attractors which essentially depend on the mental state of a person. In experiments it is shown in the form of sight effects, which are considered in the report as a test model on experimental data.

Complex biological systems demonstrate uninterrupted chaotic changer of every components xi of all system state x(t). There fundamental specificy is uninterrupted absent of it’s stationary regime forevery xi meany dx/dt≠0 and function distribution f(x) forevery number of xi for every patients and for all group of patients. For every statie state (like tremor) we can present the region of phase space like VG (quasiattractor) where (in VG) the vector x(t) present the chaotic movements. In fact, every homeostaz is equal to postural tremor or tepping hen it’s parameters creluds into quasiattractor volime. Now we demonstrate the stationary state (as regime) according to tremor or tepping. Their parameters xi indudes into some quasiattractor and we can present the evolution of tremor of patients when we can change their psichophysiological parameter under some external some external sound influence. Sound cam change the physiological parameters of human organism and as a result – the tremor parameters and it’s quasiatractor.