Systems Of Third Type Research Articles

Нестационарная стационарность систем третьего типа и философия нестабильности

There are several criteria in science for stationarity (stability) of different dynamical systems. The stationarity in physics, engineering and chemistry is being interpreted as matching the requirements of dx/dt=0, where x=x(t) - is the vector of system’s state, or the equality of distribution functions f(x) for different samples which characterize the system. However, in case of social or biological systems the matching of the requirements is impossible and there is a problem of specific assessment of stationary regimes of complex systems of the third type. The possibility of studying of such systems within the frame of deterministic chaos, stochastic approach and theory of chaos and self-organization is being discussed. This article explains why I.R. Prigogine refused from materialistic (in fact deterministic) approach in the description of such special systems of third type and tried to get away from the traditional science in the description of biological systems.

Математические модели эволюции антропометрических параметров учащихся Югры и республики Башкортостан

The evolution of biological systems on the example of changes in anthropometric indicators of the three age groups of pupils Ugra and Bashkortostan Republic from the perspective of theory of chaos and self-organization is considered. The kinematic parameters of complex systems (systems of third type) based on the motion simulation system of the state vector x(t) in the phase space of state were calculated. A special mathematical apparatus for calculation of the centers of quasi-attractors (areas of phase space in which x(t) changes continuously) and the rate of evolution was used. The authors demonstrated the calculations of the quasi-attractors’ volumes, the coordinates of their centers, as well as the velocity of these centers and the rate of evolution of biological systems in the phase space of states. A comparative analysis of the kinematic characteristics of students of Ugra and Bashkortostan Republic showed significant differences in the dynamics of anthropometric parameters.

Третья глобальная парадигма в медицине, математике и философии

Realizing the realities of the systems of third type – STT is gradually approaching the society of “skeptical” scientists, i.e. firm supporters of determinism and stochastic. Therefore the need for a brief presentation of the third paradigm of theory of chaos and self-organization in all their diversity increases many times. It is possible to express the hope that this will lead to a change in not only science but also in consciousness (view of the natural world). The proof of differences of theory of chaos and self-organization (TCS), objects (STT) from objects of deterministic and stochastic approaches (paradigms) – DSP is needed. Furthermore, a demonstration of pointlessness use of methods and theories of DSP in describing the STT. These all requires the synergy of mutual tolerance by all scientists. We must move away from the revolution in T. Kuhn’s paradigm shift to synergy and parallel existence of three global paradigms (deterministic, stochastic and third – syn-ergetic). As in nature, there are (and will be) three types of systems and in science there should be three different approaches, three paradigms. V.S. Stepin talked about these things representing postnonclassic.

Другой мир, другая наука, другие модели в описании Complexity

The understanding of very special systems of third type was created according to W.Weaver efforts. The new theory of chaos – self- organization was created last 40 years and was based on other understanding of stationary mode of third type of systems and its very specific chaotic behavior. The analog of the systems with physical system was discussed too. The third type of systems (opposite of deterministic and stochastic systems) was presented. It was discussed the principle distinguishes between dynamics of such system and traditional systems according to Heisenberg uncertainty principle. Traditional systems have certain and reproducible initial state of its system’s state vector and we can predict its future states. But in the third type of systems the authors have uncertain initial system state and uncertain vector states. It is a unique system which I.R. Prigogine in his famous article to the future generation determines as systems behind the science. The time for researching of such systems has come. For the modeling of biosystems, the authors propose method of quasi-attractor and define five special properties of complex systems. The main of it is connected with uninterrupted chaotic movements (glimmering property) of system’s vector in phase space of state and evolution of such system’s state vector in phase space of state. It was demonstrated that Heizenberg principle of uncertainty has special analog at theory of chaos – self organization. The botton boarder of the left side of inequality for the systems of third type the authors propose the value of quasiattractors, inside of it we chaos uninferrupled and chaotic movements of systems state vector. The value of quasiattractor determine like multiplication of coordinat x its speed dx/dt.

Стационарные режимы поведения сложных биосистем в рамках теории хаоса-самоорганизации

Traditional biological science (biophysics, systems analyses of biosystems) stationary mode of biosystems describes according to equation dx/dt=0 for the systems state vector x=x(t)=(x1, x2,…xm)T. But real biosystems demonstrated uninterrupted chaotic dynamics when dx/dt≠0 is always uninterrupted. The authors present two types of approaches to stationary mode investigation for biosystems. The first approach is based on the compartmental-cluster theory and the second approach is based on the theory of chaos-self-organization. The last is more convenient for real biosystems description because there are pragmatic results of its use. The compartmental-cluster approach may be used for real complex biosystems and the authors present some typical examples of such theory. The stationary mode of hierarchical neural networks were illustrated according to specific audi - analyzator. It was demonstrated that short intervals of tremogram demonstrate the real difference of distribution function parameters. As a result of such experiments – the classical statistics methods don’t usefulness for investigation of postural tremor. The tremogram, cardiogram, encephalogram are the systems of third type. The main idea consists of uninterrupted chaotic movements (glimmering property) of system’s vector in phase space of state and evolution of such system’s state vector in phase space of state. The glimmering property and evolution don’t have properties which can be modeled by traditional deterministic and stochastic approaches.

Математические основы глобальной нестабильности биосистем

The article presents features of modelling of complex systems – complexity. Specific systems of third type have no repetitions of distribution functions (and their measures), no repetitions of initial states (but the probability theory requires initial states to be repeated and experiences should be repeated many times), no certainties in prediction of the future state of a complex system, i.e. sys-tem is constantly changing and unpredictable. There is a question: what should we work with such systems, how to describe and predict them? Deterministic and stochastic approaches are useless. I.R. Progogine thought that such unique systems are not objects of the science. It is very important that the chaos that demonstrates regulation of tremor, tapping, heart rate beats, myograms and electroencephalograms does not suit to Lorenz attractor, or model chaos in chaos theory (because there are no certain initial states and parameters of quasi-attractors of the same subject (a human) cannot be repeatable). In models of traditional chaos these parameters are repeatable, the Lyapunov exponents can be calculated and autocorrelation functions coincide). But in our case everything is opposite: the autocorrelation functions are unstable, the Lyapunov exponents cannot be calculated, and there are no models. The authors suggest calculating volumes of quasi-attractors.