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We show convergence of a procedure for multiple training of a neural network, when during multiple repetitions of the solution of a binary classifi cation task based on unchanged packets of training samples the neural emulator can initially demonstrate a chaotic set of values for the feature weights, which as the number of iterations increases is reduced to a certain ranked series. Keywords: biosystem, order parameters, neural network, theory of chaos and self-organization.Development of synergetics has been associated with the possibility and need for solving problems involving identifi cation of order parameters and constructing a theory of systems synthesis as a whole. Despite tremendous efforts by scientists over the past 40 years, there have been no substantial achievements in the area of formalization of the procedure for identifi cation of order parameters and total systems synthesis. Identifi cation of order parameters remains a unique procedure for individual selected tasks. Universal formalization of systems synthesis is lacking at the moment for complex systems, which especially include biosystems [1,2].At the same time, there is a certain class of tasks and systems where such formalization is possible by application of neural network technologies. In recent years, neural emulators have been widely used for identifi cation of the most important diagnostic signs (features) in medicine and biology, but the result obtained with their application is not always unambiguous, and so it has not been worthwhile to use neural emulators for practical purposes. Is there a way out of this situation? An answer is presented in this paper, using binary classifi cation as an example, i.e., for attempts to identify order parameters and to rank the weights of diagnostic features: the components x i of the system state vector x = x(t).Nonparametric Distribution of Weighted Features in a Neural Emulator. The binary classifi cation task utilizing a neural computer is very widely used in medicine, since it lets us, without separate analysis of the dynamics of variation in each component x i of the state vector for the human body (the human state vector) x = x(t) = (x 1 , x 2 , ..., x m ) T , to establish in general how one group of patients (for example, an untreated group) differs from another group (with a specifi c type of treatment). Based on binary classifi cation, we can compare groups of patients receiving different types of care (drugs, physical therapy, etc.) [2, 3] and can establish the effi cacy of health-related measures and the effect of environmental factors, and to evaluate coaching in sports.After identifi cation of the differences by the neural emulator, we need to estimate the signifi cance (weight) of a specifi c ith diagnostic feature (i = 1, 2, ..., m, where m is the dimensionality of the phase space), i.e., the components x i of the human state vector, which is especially important when these features characterize the state of different functional systems in the human body. Guidelines for the doctor (wh...

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Now it is evident that nature and society have a great number of special systems which very differ from traditional objects (systems) of physics, chemists and engineering. For such special (synergetic-chaotic) systems we propose the special third paradigm and construct five basic properties of (unique) systems and on 13 differences in the methods, basic concepts about such systems. The introduction of such basic properties and differences are presented in the article. We postulate the humanity evolution, dynamic of social and political systems, biosphere of Earth, the human organism and his functional systems and many other systems (Universe at all) have all five such properties and must be described according to special synergetic paradigm. Now the authors presents all these special properties and the special table where the differences between deterministic-stochastic systems (and its theoretical approaches) and the synergetic systems (complexity, self-organization systems) were presented more conveniently.

This article examines the problem of standardizing the states of complex dynamic objects -dynamic biological systems (DBIs). The resolution of this problem reduces to using mathematical models of these and analyzing the dynamic processes in DBIs in response to specially identified optimum parameters (amplitude, duration) of external (electrical, mechanical, chemical) stimuli. The potential for the use of such approaches in medicine and biology is also discussed.The formalization of biomedical research is a process that is still far from completion. The use of mathematical methods in such investigations along with various mathematical models of the biological systems being studied is still in the developmental stage. The mathematical methods that are used are usually based on statistical analyses of data and the determination of numerical characteristics of the expected distribution function of a given random variable -moments of different orders (mathematical expectation, variance, modes) or correlation coefficients [1, 2].However, it is still relatively rare for researchers to attempt to construct mathematical models of the dynamics of medical-biological processes, and when this is done the model is sometimes regarded as an exception to the rule and a mathematical oddity. This situation is first of all the result of the lack of a unified approach to the mathematical representation of biomedical processes, as well as to the cautious attitude of specialists in biology and medicine as regards the use of math -specialists who tend to be advocates of pure empiricism. Despite advances in mathematics and biophysics and the work of researchers in neurocomputing and systems analysis, no significant strides are being made in medical schools or university biology programs in the teaching of physico-mathematical methods of studying living things. The efforts here are weak and disorganized. The importance of the use of rigorous methods in research and the standardization of biomedical measurements is not being stressed, and students are not being fully exposed to the possibilities of mathematical methods of studying the functional systems of humans and animals. Graduates in the biomedical fields finish their schooling with the firm conviction that the issues of precision in measurement and metrological evaluation of the equipment they use are the concerns of other specialists. The blame for poor-quality measurements in biology and medicine must be laid at the foot not of these specialists, but those working in biology and medicine.The "consumer's" attitude of doctors and biologists toward technical systems obviously can only be changed through the efforts of specialists in metrology and physics together with mathematicians and engineers. The disciplines mentioned above must be better incorporated into the training programs for doctors and biologists (in the form of special courses on metrology, neurocomputing, and mathematical methods). Otherwise, the gap between these two areas of intellectual activity will only widen, a...

Work of artificial neural networks does not ensure the identification of order parameters (which are the principal diagnostic characters xi in biomedicine). We suggest to eliminate the 1st type uncertainties (when samplings xi statistically match for different physiological states of a human body) by introducing random setting of initial weight values wio of xi and subsequent multiple repetition (n≥1000) of artificial neural network settings. The xi ranking is made according to the weight samplings wi collected after such settings are applied.

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What does it mean: certainty and uncertainty, chaos and order? The understanding of such definition and real interpretation of chaotic behavior the third type of systems in nature was presented. The practical realization of different medical problems was presented too.