HOMEOSTATIC SYSTEM CAN NOT BE DESCRIBED BY STOCHASTICS OR DETERMINISTIC CHAOS
Authors:
Type:
Article
Pages:
from 28
to 33
Status:
Published
Received:
28.12.2015
Accepted:
28.12.2015
Published:
28.12.2015
Language:
Russian
Keywords:
living systems, autocorrelation, phase space, complexity.
Abstract (English):
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.
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.
Keywords:
living systems, autocorrelation, phase space, complexity.
living systems, autocorrelation, phase space, complexity.
Живые системы – системы третьего типа (СТТ) по W. Weaver (организованная сложность) [18] имеют особую динамику поведения их вектора состояния x=x(t)=(x1, x2, …,xm)T в m‐мерном фазовом пространстве состояний (ФПС). До настоящего времени многие пытались СТТ описывать терминами статистической функции распределения f(x) или в рамках теории детерминированного хаоса Лоренца – Арнольда.
