Stochastic processing of chaotic dynamics outcome of biomechanical parameters in human

2015 ◽  
Vol 4 (1) ◽  
pp. 31-39
Author(s):  
Берестин ◽  
D. Berestin ◽  
Игуменов ◽  
D. Igumenov ◽  
Рассадина ◽  
...  
Keyword(s):  
Distribution Function ◽  
Stochastic Analysis ◽  
Chaotic Dynamics ◽  
Involuntary Movement ◽  
Deterministic Chaos ◽  
Special Kind ◽  
Stochastic Processing ◽  
Biomechanical Parameters ◽  
Distribution Shifts ◽  
Non Parametric

The results of the stochastic analysis of postural tremor (as alleged involuntary movement) and tapping (as supposedly voluntary movement) are considered in a comparative perspective. It is proved that the stochastic analysis of the results of chaotic dynamics in tremorogramms and tapping does not give significant differences (absence of voluntariness). Typically, all samples are significantly different and it is impossible to distinguish subjects in their tremorogramms or tapingramm. The significant differences between sites of tremorogramms in terms of a normal distribution or a non-parametric distribution are demonstrated. A continuous variation of the distribution function is observed: parametric distribution shifts to non-parametric distribution, but among themselves they (distribution function) are all different. It is well known that the unpredicta-bility and continuing changes in the state are characteristic feature of chaos. The evidence of special kind of chaos in biosystems which differs significantly from the deterministic chaos of Tom – Ar-nold is given.

DETERMINISTIC CHAOS IN AN INTERPHASE LAYER OF A LIQUID–VAPOR SYSTEM

2004 ◽  
Vol 14 (10) ◽  
pp. 3671-3678
Author(s):  
G. P. BYSTRAI ◽  
S. I. IVANOVA ◽  
S. I. STUDENOK
Keyword(s):  
Phase Transitions ◽  
Chaotic Dynamics ◽  
Deterministic Chaos ◽  
Second Order ◽  
Homogeneous Layer ◽  
Time Interval ◽  
Evaporation And Condensation ◽  
Starting Conditions ◽  
Kolmogorov's Entropy ◽  
Dimensional Mapping

A second-order nonlinear differential equation with an aftereffect for the density of a thin homogeneous layer on a liquid and vapor interface is considered. The acts of evaporation and condensation of molecules, which are regarded as periodic "impacts", excite the layer. The mentioned NDE is integrated over a finite time interval to find a 2D (two-dimensional) mapping whose numerical solution describes the chaotic dynamics of density and pressure in time. The algorithms of constructing bifurcation diagrams, Lyapunov's exponents and Kolmogorov's entropy for systems with first-order, second-order phase transitions and Van der Waals' systems were elaborated. This approach allows to associate such concepts as phase transition, deterministic chaos and nonlinear processes. It also allows to answer a question whether deterministic chaos occurs in systems with phase transitions and how fast the information about starting conditions is lost within them.

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.

scholarly journals Nonuniform Chaotic Dynamics and Effects of Noise in Biochemical Systems

1987 ◽  
Vol 42 (2) ◽  
pp. 136-142 ◽  
Author(s):  
H. Herzel ◽  
W. Ebeling ◽  
Th. Schulmeister
Keyword(s):  
Chaotic Dynamics ◽  
Chaotic Systems ◽  
Quantitative Description ◽  
Deterministic Chaos ◽  
Correlated Noise ◽  
Sustained Oscillations ◽  
Exponential Separation ◽  
Biochemical Systems ◽  
Relative Robustness

Biochemical models capable of sustained oscillations and deterministic chaos are investigated. Chaos is characterized by exponential separation of near-by trajectories in the long-term average. However, we observed rather large deviations from purely exponential separation termed "nonuniformity". A quantitative description and consequences of nonuniformity are discussed.Furthermore, the influence of short-correlated noise is treated using next-amplitude maps and Lyapunov exponents. Drastic amplification of fluctuations in non-chaotic systems and relative robustness of chaos were found.

Chaos: An Ecological Reality?

1998 ◽  
Vol 08 (06) ◽  
pp. 1325-1333 ◽  
Author(s):  
Ranjit Kumar Upadhyay ◽  
S. R. K. Iyengar ◽  
Vikas Rai
Keyword(s):  
Chaotic Dynamics ◽  
Dynamical Behavior ◽  
Natural Populations ◽  
Deterministic Chaos ◽  
Ecological Systems ◽  
Biological Interactions ◽  
Simulation Experiments ◽  
Analysis Techniques ◽  
Ecosystem Evolution ◽  
Novel Applications

Deterministic chaos has been studied extensively in various fields. Some of the ideas emerging out of these studies have been put to novel applications. However, it is unknown whether natural ecological systems support chaotic dynamics. There is no concrete evidence which suggests that ecosystem evolution is chaotic in certain situations. This is very intriguing because ecosystems do possess all the necessary qualifications to be able to support such a dynamical behavior. The present paper attempts to answer the above question with the help of a few systems modeling different but very common ecological situations. A new methodology for the analysis of a class of model ecological systems is presented. Simulation experiments suggest that natural terrestrial systems are not suitable candidates where one should look for chaos. Additionally, our study also points out that the failure of attempts to observe chaos in natural populations might have resulted because biological interactions are not conducive for such a behavior to be supported. The cause of these failures may not be the poor data quality or demerits in the analysis techniques.

scholarly journals Evolutionary geomorphology: thresholds and nonlinearity in landform response to environmental change

2006 ◽  
Vol 3 (2) ◽  
pp. 365-394 ◽  
Author(s):  
J. D. Phillips
Keyword(s):  
Chaotic Dynamics ◽  
Deterministic Chaos ◽  
Dynamical Instability ◽  
Historical Contingency ◽  
Number Of Factors ◽  
External Forcings ◽  
History Matter ◽  
Path Dependent ◽  
Prediction Techniques ◽  
Response To Environmental Change

Abstract. Geomorphic systems are typically nonlinear, owing largely to their threshold-dominated nature (but due to other factors as well). Nonlinear geomorphic systems may exhibit complex behaviors not possible in linear systems, including dynamical instability and deterministic chaos. The latter are common in geomorphology, indicating that small, short-lived changes may produce disproportionately large and long-lived results; that evidence of geomorphic change may not reflect proportionally large external forcings; and that geomorphic systems may have multiple potential response trajectories or modes of adjustment to change. Instability and chaos do not preclude predictability, but do modify the context of predictability. The presence of chaotic dynamics inhibits or excludes some forms of predicability and prediction techniques, but does not preclude, and enables, others. These dynamics also make spatial and historical contingency inevitable: geography and history matter. Geomorphic systems are thus governed by a combination of ''global'' laws, generalizations and relationships that are largely (if not wholly) independent of time and place, and ''local'' place and/or time-contingent factors. The more factors incorporated in the representation of any geomorphic system, the more singular the results or description are. Generalization is enhanced by reducing rather than increasing the number of factors considered. Prediction of geomorphic responses calls for a recursive approach whereby global laws and local contingencies are used to constrain each other. More specifically a methodology whereby local details are embedded within simple but more highly general phenomenological models is advocated. As landscapes and landforms change in response to climate and other forcings, it cannot be assumed that geomorphic systems progress along any particular pathway. Geomorphic systems are evolutionary in the sense of being path dependent, and historically and geographically contingent. Assessing and predicting geomorphic responses obliges us to engage these contingencies, which often arise from nonlinear complexities. We are obliged, then, to practice evolutionary geomorphology: an approach to the study of surface processes and landforms with recognizes multiple possible historical pathways rathen than an inexorable progression toward some equilbribrium state or along a cyclic pattern.

Homeostatic System Can Not Be Described by Stochastics or Deterministic Chaos

2015 ◽  
Vol 22 (4) ◽  
pp. 28-33 ◽  
Author(s):  
Полухин ◽  
V. Polukhin ◽  
Еськов ◽  
V. Eskov ◽  
Эльман ◽  
...  
Keyword(s):  
Distribution Function ◽  
Stationary State ◽  
Natural Science ◽  
Invariant Measures ◽  
Deterministic Chaos ◽  
Living Systems ◽  
Deterministic Approach ◽  
The Third ◽  
Rate Of Increase ◽  
Mixing Property

The living systems (complexity, homeostatic systems) are a special systems of the third type of complexity in natural science and for such systems it is impossible to determine the stationary state in form of dx/dt=0 (deterministic approach) or in the form of invariance of distribution function f(x) for samples acquired in a row of, the any component xi of all vectors of state x=x(t) =(x1,x2,…,xm)T in m‐dimensional phase space of states. At the same time the mixing property doesn’t met (no invariant measures), the autocorrelation functions A(t) don’t tend to zero if t→∞, Lyapunov’s constants can continuously change the sign. Such systems of the third type (complexity) do not meet the condition of Glansdorff – Prigogine’s theorem, i.e. P ‐ the rate of increase of entropy E (P=dE/dt) doesn’t minimized near the point of maximum entropy E (i.e., at point of thermodynamic equilibrium). It is proposed to use the concept of quasi‐attractors to describe the complexity.

Dynamics of Pool Boiling on Plain and Nanotube Coated Silicon Surfaces

2010 ◽  
Author(s):  
Vijaykumar Sathyamurthi ◽  
Debjyoti Banerjee
Keyword(s):  
Heat Flux ◽  
Surface Temperature ◽  
Chaotic Dynamics ◽  
Pool Boiling ◽  
Deterministic Chaos ◽  
Nucleate Boiling ◽  
High Heat ◽  
Heat Fluxes ◽  
Film Boiling ◽  
Test Fluid

Saturated pool boiling experiments are conducted over silicon substrates with and without Multi-walled Carbon Nanotubes (MWCNT) with PF-5060 as the test fluid. Micro-fabricated thin film thermocouples located on the substrate acquire surface temperature fluctuation data at 1 kHz frequency. The high frequency surface temperature data is analyzed for the presence of chaotic dynamics. The shareware code, TISEAN© is used in analysis of the temperature time-series. Results show the presence of low-dimensional deterministic chaos, near Critical Heat Flux (CHF) and in some parts of the Fully Developed Nucleate Boiling (FDNB) regime. Some evidence of chaotic dynamics is also obtained for the film boiling regimes. Singular value decomposition is employed to generate pseudo-phase plots of the attractor. In contrast to previous studies involving multiple nucleation sites, the pseudo-phase plots show the presence of multi-fractal structure at high heat fluxes and in the film boiling regime. An estimate of invariant quantities such as correlation dimensions and Lyapunov exponents reveals the change in attractor geometry with heat flux levels. No significant impact of surface texturing is visible in terms of the invariant quantities.

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