Complexity. Mind. Postnonclassic Complexity. Mind. Postnonclassic Сложность. Разум. Постнеклассика 2306-174X 4173 10.12737/6725 Математика в описании хаоса и синергетических систем Mathematics in Description of Chaos and Synergetic Systems Математика в описании хаоса и синергетических систем New estimation method of degree of chaos in biosystems Новый метод оценки степени хаотичности биосистем Горленко Н. П. Gorlenko N. П. Кощеев В. П. Koshcheev V. П. Бурыкин Ю. Г. Burykin Yu. Г. Еськов В. В. Eskov Valeriy V. z.asconcrete@gmail.com Пашнин А. С. Pashnin A. С. 02 12 2014 02 12 2014 3 3 69 77 https://zh-szf.ru/en/nauka/article/4173/view

Демонстрируется невозможность использования традиционных стохастических методов в оценке параметров сложных биосистем – complexity. Их амплитудно-частотные характеристики, автокорреляционные функции A(t), экспоненты Ляпунова, статистические функции распределения f(x) непрерывно изменяются. На фоне такой хаотической динамики параметров треморограмм, кардиограмм, теппинграмм, миограмм и др. параметров гомеостаза можно наблюдать некоторую упорядоченность в динамике этих процессов. Эта упорядоченность проявляется в изменениях числа пар совпадений выборок, которые получаются при измерениях указанных процессов. Поскольку все стохастические характеристики непрерывно изменяются, то предлагается использовать расчет статистических функций распределения при повторах серий одинаковых экспериментов. В этом случае число совпадений пар выборок (возможности их отнесения к одной генеральной совокупности) будет количественно представлять механизм перехода от хаоса к порядку или изменения до-ли хаоса в организации движений и биоэлектрической активности мышц. Демонстрируется ряд характерных примеров из области сравнения матриц парного сравнения при различных физиологических состояниях организма обследуемых испытуемых.

. Potential application of traditional and stochastic methods in assessment of parameters of complex biosystem – complexity is presented. Their amplitude-frequency characteristics, autocorrelation functions A(t), Lyapunov exponents, statistical distribution function f(x) constantly change. In spite of such chaotic dynamics in recorded parameters of tremor, tapping, cardiograms, myograms and other parameters of homeostasis, an order in the dynamics of these processes can be observed. The order is revealed in a change of numbers of sample overlaps that are obtained as a result of some processes. Owing to all the stochastic characteristics constantly change, calculation method for statistical distribution functions with repetitions of identical experimental sets is proposed. In this case, number of sample overlaps (their belonging to the same general population) will numerically present the transition mechanism to order out of chaos or the variation of chaos degree in movement formation and electrobiological muscular activity. The current work shows some typical examples of different physiological human states presented in a form of matrices of paired comparison.

гомеостаз квазиаттрактор треморограмма тепинграмма homeostasis quasiattractor tremor tapping

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