Complex System Stationary Mode According to the Theory of Chaos-Self-Organization

10.12737/3329 ◽  
2014 ◽  
Vol 21 (1) ◽  
pp. 141-144
Author(s):  
Бикмухаметова ◽  
L. Bikmukhametova ◽  
Полухин ◽  
L. Polukhin ◽  
Вохмина ◽  
...  
Keyword(s):  
Phase Space ◽  
State Vector ◽  
Chaotic Dynamics ◽  
Main Idea ◽  
Self Organization ◽  
Stationary Mode ◽  
Cluster Approach ◽  
Classical Statistics ◽  
Complex Biosystems ◽  
Real Complex

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.

Statistical and evaluation chaotic parameters under cardio exertion

2015 ◽  
Vol 4 (2) ◽  
pp. 5-10
Author(s):  
Филатова ◽  
D. Filatova ◽  
Карпин ◽  
Vladimir Karpin ◽  
Еськов ◽  
...  
Keyword(s):  
Phase Space ◽  
Cardiovascular System ◽  
Chaos Theory ◽  
Chaotic Dynamics ◽  
Stochastic Approach ◽  
Dynamic Exercise ◽  
Self Organization ◽  
Dimensional Phase Space ◽  
Classical Statistics ◽  
Fitness Indicators

Methods of classical statistics and the theory of chaos and self-organization studied the behavior of the vector of the cardiovascular system in groups of students trained and untrained in response to dosed physical stress .It was found that students without physical fitness indicators of cardio area quasi-attractors increased after exercise . The study had shown significant changes in the dynamics of the behavior of the parameters of functional systems of the human body compared to the stochastic approach based on the histogram and Shannon entropy . It is shown the feasibility of application of chaos theory, self-organization in the evaluation of the reaction of the cardiovascular system of the person on the dynamic exercise. As a measure of the cardiovascular system of the person (to load and after the load) used quasi-attractor motion of the state vector of the system in the two-dimensional phase space of states. Within the framework of the theory of chaos and self-organization may determine the parameters of the spacecraft for individual subjects and their groups to compare their chaotic dynamics in time or in the phase space of states.

Other World, Other Science, Other Models in Complexity Descreaption

10.12737/3328 ◽  
2014 ◽  
Vol 21 (1) ◽  
pp. 138-141
Author(s):  
Еськов ◽  
Valeriy Eskov ◽  
Филатова ◽  
O. Filatova
Keyword(s):  
Phase Space ◽  
State Vector ◽  
Stochastic Systems ◽  
Chaotic Behavior ◽  
Future Generation ◽  
Self Organization ◽  
Stationary Mode ◽  
Initial State ◽  
Heisenberg Uncertainty Principle ◽  
The Third

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.

Two types of approaches at personification medicine development

2015 ◽  
Vol 4 (1) ◽  
pp. 81-88
Author(s):  
Филатова ◽  
O. Filatova ◽  
Хадарцева ◽  
K. Khadartseva ◽  
Еськов ◽  
...  
Keyword(s):  
Phase Space ◽  
Medical Treatment ◽  
Basic Principle ◽  
State Vector ◽  
The State ◽  
Self Organization ◽  
Human Organism ◽  
Medicine Development ◽  
State Measurement

It is evident that requirement of medical personification includes two procedures: individual (with uninterrupted procedure of human organism state measurement) diagnostics and the second part which is connected with uninterrupted control of the efficiency of medical treatment and measurements of human organism parameters. According to classic deterministic-stochastic approaches we don´t have any possibility for realization of the basic principle in medicine because every human organism has its own specific features. We conduct the diagnostics according to beha-vior of state vector of human organism in phase space of states according to every coordinates of human´s state vector and with calculation of quasiattractors. It was presented new bioinformational methods and software for calculation of quasiattractors parameters for dissolving such contradic-tions between deterministic-stochastic medicine and the use of theory of chaos self-organization where the state vector of human organism demonstrates uninterrupted movements. The practical results of such procedure are also presented according to the theory of chaos self-organization.

Possibilities of stochastic processing of system parameters with chaotic dynamics

10.12737/5519 ◽  
2014 ◽  
Vol 3 (2) ◽  
pp. 59-67
Author(s):  
Берестин ◽  
D. Berestin ◽  
Попов ◽  
Yuriy Popov ◽  
Вохмина ◽  
...  
Keyword(s):  
Phase Space ◽  
General Population ◽  
Chaotic Dynamics ◽  
Estimation Method ◽  
Pairwise Comparison ◽  
Wilcoxon Test ◽  
Self Organization ◽  
Postural Tremor ◽  
System Parameters ◽  
Stochastic Processing

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.

Assessment of parameters state of neuromuscular cluster in the conditions of the dosed physical activity

10.12737/3860 ◽  
2014 ◽  
Vol 8 (1) ◽  
pp. 1-6
Author(s):  
Рассадина ◽  
Yu. Rassadina ◽  
Попов ◽  
Yuriy Popov ◽  
Карпин ◽  
...  
Keyword(s):  
Physical Activity ◽  
Control System ◽  
Phase Space ◽  
State Vector ◽  
Self Organization ◽  
Neuromuscular System ◽  
Two Dimensional ◽  
Practical Possibility ◽  
Dimensional Phase Space ◽  
State Vector Of System

Parameters of neuromuscular system at the unexercised and trained examinees from a position of the theory of chaos and self-organization are studied. Essential distinction between two studied groups (the trained and unexercised students) is established. Dynamics of involuntary micro-movements of extremities (fingers of hands) in a person as reaction to the dosed physical activity is shown in change of parameters of quasiattractors of characteristics of a tremor. Dynamics of increase in volumes of quasiattractors of a vector of organism state in the unexercised students is revealed. The new technique of research of a control system by movements of a person by means of the analysis of characteristics of a tremor of an extremity in the conditions of physical activity is stated. Practical possibility of application of the method of multidimensional phase spaces of involuntary micro-movement in the assessment of reaction of neuromuscular system of the person on dynamic physical activity is shown. As a measure of state of human neuromuscular system (to loading and after loading) the authors use the quasiattractors of movement of state vector of system in two-dimensional phase space of states.

scholarly journals Simulation of Human Limb Movement

2020 ◽  
pp. 32-43
Author(s):  
Dmitriy Gorbunov
Keyword(s):  
Experimental Data ◽  
Simulation Model ◽  
Chaotic Dynamics ◽  
Random Number Generation ◽  
Mathematical Statistics ◽  
Self Organization ◽  
Mathematical Form ◽  
Model Data ◽  
Initial State ◽  
Complex Biosystems

Simulation of any processes is based on some laws that take place inside the simulated object and outside it (changing the environment in which the object is located). In the study of complex biosystems, the identification of patterns is complicated by the fact that such systems have a chaotic structure. In such systems, it is impossible to arbitrarily repeat the initial state xi, any intermediate xn and final xk. Simulation of complex biosystems should be based on random patterns. The created simulation model works based on the random number generation. There are no static values in the model. The inclusion of regulatory mechanisms of the model is based on the search of F-solutions. Chaotic dynamics of changes in the trajectory of a person's limb is established based on experimental data. In accordance with this, in the simulation model, the level of limb retention in space changes its direction by random images in real time. In the framework of the above patterns, a mathematical model of the interaction of muscle bundles was developed to solve the problem of holding the limb in space. When analyzing the performance of the simulation model, the basis of the evaluation measure was taken. The results were obtained on the basis of mathematical statistics and the calculation of the quasiattractor parameters in the framework of the theory of chaos and self-organization. As a result, the correspondence of experimental and model data was established. In the framework of mathematical statistics, when constructing matrices of paired comparisons for experimental data, the number of pairs of matches (the word "matches" refers to the possibility of assigning the compared pairs of samples to one general set) is k = 11 %. The same number of coincidence pairs in percentage terms was established when comparing model data and model with experimental data. In the framework of the theory of chaos and self-organization, the quasiattractor parameters coincide in their area and visual assessment of phase planes. As a result of the research, high accuracy of the model is established, which is ensured by some chaotic dynamics of the model with chaotic selfregulation mechanisms. There are no constants in the mathematical form of the simulation model, which ensures the reproduction of N.A. Bernstein "repetition without repetition" hypothesis, which has been proven for experimental data. For theoretical biophysics, the constructed simulation model is able to provide understanding of the neuromuscular system functioning, as well as, with some complication and expansion of the algorithm, the central nervous system.

Parameters quasiattractors cardiova.scular system of the subjects in the conditions of the dosed physical load

10.12737/7648 ◽  
2014 ◽  
Vol 3 (4) ◽  
pp. 4-12
Author(s):  
Яхно ◽  
V. Yakhno ◽  
Карпин ◽  
V. Karpin ◽  
Кощеев ◽  
...  
Keyword(s):  
Physical Activity ◽  
Phase Space ◽  
Cardiovascular System ◽  
Human Body ◽  
Chaotic Dynamics ◽  
Calculation Of Parameters ◽  
New Methods ◽  
Methods Of Calculation ◽  
Classical Statistics ◽  
Neuromuscular Systems

Parameters of cardiovascular system at the unexercised and trained examinees by methods of classical statistics and new methods of calculation of chaotic dynamics of behavior of a vector of a condition of a human body in phase space are studied. The tendency to increase in the area of quasiattractors of unexercised examinees after physical activity is shown that is also confirmed by change of values of volumes of quasiattractors after loading in comparison with data to loading. Long physical activity (training) stabilizes parameters of cardiovascular and neuromuscular systems of the trained students in aspect of natural changes of parameters of quasiattractors, and their dynamics shows fitness degree. Calculation of parameters of quasiattractors of cardiovascular system allows to estimate objectively dynamics of reserve opportunities of an organism and their predictive importance.

Analysis of Myograms Acording to the Stochastics and the Chaos Theory – Self-Organization

2015 ◽  
Vol 22 (2) ◽  
pp. 32-38
Author(s):  
Григоренко ◽  
V. Grigorenko ◽  
Горбунов ◽  
D. Gorbunov ◽  
Еськов ◽  
...  
Keyword(s):  
Phase Space ◽  
Shannon Entropy ◽  
Chaos Theory ◽  
The State ◽  
Biomechanical Analysis ◽  
Self Organization ◽  
Biological Research ◽  
Dimensional Phase Space ◽  
Low Load ◽  
Little Finger

The paper shows the feasibility of applying the method of multi-dimensional phase space as a quantitative measure for the evaluation of chaotic dynamics on the example of the muscles (flexor of the little finger). The method of multi-dimensional phase space was used. In the study and modeling of complex biological objects (complexity) there is the possibility of introducing traditional physical methods in biological research and new methods based on the chaos theory and self-organization. As a measure of the state of the neuromuscular system of the person (weak muscle tension and strong, almost the maximum force), the authors used quasi-attractors volumes of multidimensional phase space. This enables identification of the actual measurements of the parameters of the functional state with weak muscles (Fi = 5 daN) and strong (Fi = 10 daN) static stress. The authors built a timebase signal received from the electromyograph and the autocorrelation function A(t) of signal. A biomechanical analysis of the state of the system is carried out on the basis of comparison of the volume VG quasi attractor, as well as on the basis of the analysis of the Shannon entropy E. Volume of quasi attractor VG displacements under low load is slightly less than the same volume displacement VG with strong exertion of the muscles of the flexor of the little finger, exactly the same as the values of the Shannon entropy under a heavy load increases compared to the values obtained under low load the muscles.

Homeostasis and Evolution From the Standpoint of the Third Paradigm

2015 ◽  
Vol 22 (3) ◽  
pp. 33-39
Author(s):  
Филатова ◽  
O. Filatova ◽  
Еськов ◽  
Valeriy Eskov ◽  
Хадарцев ◽  
...  
Keyword(s):  
Heart Rate ◽  
Numerical Investigation ◽  
State Vector ◽  
Stationary Regime ◽  
Living System ◽  
Self Organization ◽  
New Paradigm ◽  
Statistical Function ◽  
The Third ◽  
New Interpretation

According to new theory of chaos - self organization if was presented new paradigm of homeostasis and evolution. Numerical investigation of tremor, miogram, encephalograms, heart-rate, etc. proved the simultaneously changing of experimental results as dx/dt=0 for the special human state vector x(t) for different interval of time At. The statistical function of x(t) -fix) present the simultaneously changing of/(x). So the homeostasis seems as a stationary regime when the parameters of quasi-attractor are not change. The authors present the new interpretation of homeostasis and evolution for special systems with special dynamic of living system (hymen lodi special). Then the first place take the x(t) parameters of such special third type of system.

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