Possibilities of stochastic processing of system parameters with chaotic dynamics

D. Berestin; Yuriy Popov; Yu. Vokhmina; K. Khadartseva

doi:10.12737/5519

POSSIBILITIES OF STOCHASTIC PROCESSING OF SYSTEM PARAMETERS WITH CHAOTIC DYNAMICS Possibilities of stochastic processing of system parameters with chaotic dynamics

АА Аа

Published in Complexity. Mind. Postnonclassic · Volume 3, Issue 2 · Pages 59–67 · Rubric: Mathematics in Description of Chaos and Synergetic Systems

DOI: https://doi.org/10.12737/5519

Received: 29.08.2014 Accepted: 21.11.2014 Published: 21.11.2014 Language of publication: RUS

Authors

D. Berestin

Yuriy Popov

Yu. Vokhmina

K. Khadartseva

D. Berestin

Yuriy Popov

Yu. Vokhmina

K. Khadartseva

ABSTRACT

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.

KEYWORDS

phase space of states, quasi-attractors, stochastics, chaos.

Text

Особые системы третьего типа (СТТ) представляют все виды многоклеточных организмов, у которых имеются хотя бы некоторые аналоги нервной системы и органы, работа которых зависит от работы этих разных видов нервной системы. На примерах функционирования различных биосистем, управляемых центральной нервной системой человека (а это биомеханика, работа сердца, биохимического гомеостаза и многих других функциональных систем), мы убедительно доказали правоту второго постулата теории хаоса-самоорганизации, который был высказан В.М. Еськовым 30 лет назад: конкретное состояние биосистемы информационно незначимо и точка (состояние биосистемы в момент времени t) в фазовом пространстве не может описывать состояния СТТ - complexity [1,8,9].

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GOST

Berestin D., Popov Y., Vokhmina Y., Khadartseva K. Possibilities of stochastic processing of system parameters with chaotic dynamics // Complexity. Mind. Postnonclassic. 2014. no. 2. pp. 59-67. DOI: https://doi.org/10.12737/5519. (Date of access 30.09.2026).

MLA

D. Berestin, Popov Y., Vokhmina Y., Khadartseva K.. "Possibilities of stochastic processing of system parameters with chaotic dynamics." Complexity. Mind. Postnonclassic 3.2 (2014): 59-67. DOI: https://doi.org/10.12737/5519.

APA

Berestin D., Popov Y., Vokhmina Y., Khadartseva K. (2014). Possibilities of stochastic processing of system parameters with chaotic dynamics. Complexity. Mind. Postnonclassic, 3(2), 59-67. https://doi.org/10.12737/5519

Chicago

D. Berestin, Popov Y., Vokhmina Y., Khadartseva K.. "Possibilities of stochastic processing of system parameters with chaotic dynamics." Complexity. Mind. Postnonclassic 3, no. 2 (2014): 59-67. https://doi.org/10.12737/5519.

WIKI

{{cite journal | author = Berestin D., Popov Y., Vokhmina Y., Khadartseva K. | title = Possibilities of stochastic processing of system parameters with chaotic dynamics | journal = Complexity. Mind. Postnonclassic | year = 2014 | volume = 3 | issue = 2 | pages = 59-67 | doi = 10.12737/5519 }}

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POSSIBILITIES OF STOCHASTIC PROCESSING OF SYSTEM PARAMETERS WITH CHAOTIC DYNAMICS Possibilities of stochastic processing of system parameters with chaotic dynamics

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