LIVING SYSTEMS (COMPLEXITY) FROM THE POINT OF CHAOS AND SELF-ORGANIZATION THEORY
Authors:
Type:
Article
Pages:
from 25
to 32
Status:
Published
Received:
28.09.2015
Accepted:
28.09.2015
Published:
28.09.2015
Language:
Russian
Keywords:
complexity, self-organization, order parameter, living systems, quasi-attractor.
Abstract (English):
Attempts to describe complex biological systems (complexity) in terms of modern mathematics and physics continue. However, it is now evident that complexity cannot be the object of modern science because of their continuous change in the parameters and the absence of arbitrary repetition of initial parameters x (to) of any complexity. This article presents the the arguments of lack of capacity modeling of complex biophysical systems under deterministic and stochastic approaches due to the constant chaotic change of the state vector parameters x = x(t) = (x1,x2....,xm)Tof any complex biosystem (complexity). At any point of time h, the chaotic dynamics of homeostasis in signals, such as tapping tremors, electromyograms, neurograms, cardiograms, electroencephalograms, and other biochemical recordings, can be observed. During constant and chaotic changes of x(t) (i.e., dx/dteQ), the amplitude-frequency characteristics (AFC) and the autocorrelation functions A(t) constantly change. Therefore, the mixing property fails and the Lyapunov exponents can chaotically and randomly change signs. Chaos of complex biosystems differs from chaos of physical systems primarily due to the irreproducible initial value x(to). There are two methods for studying such systems: a stochastic method for processing random samples based on a matrix of pairwise comparisons and a computing method that utilizes quasi-attractor parameters, Vg for x(t), in the phase space of states. Here, such calculations are presented for biomechanics and electrophysiology.
Attempts to describe complex biological systems (complexity) in terms of modern mathematics and physics continue. However, it is now evident that complexity cannot be the object of modern science because of their continuous change in the parameters and the absence of arbitrary repetition of initial parameters x (to) of any complexity. This article presents the the arguments of lack of capacity modeling of complex biophysical systems under deterministic and stochastic approaches due to the constant chaotic change of the state vector parameters x = x(t) = (x1,x2....,xm)Tof any complex biosystem (complexity). At any point of time h, the chaotic dynamics of homeostasis in signals, such as tapping tremors, electromyograms, neurograms, cardiograms, electroencephalograms, and other biochemical recordings, can be observed. During constant and chaotic changes of x(t) (i.e., dx/dteQ), the amplitude-frequency characteristics (AFC) and the autocorrelation functions A(t) constantly change. Therefore, the mixing property fails and the Lyapunov exponents can chaotically and randomly change signs. Chaos of complex biosystems differs from chaos of physical systems primarily due to the irreproducible initial value x(to). There are two methods for studying such systems: a stochastic method for processing random samples based on a matrix of pairwise comparisons and a computing method that utilizes quasi-attractor parameters, Vg for x(t), in the phase space of states. Here, such calculations are presented for biomechanics and electrophysiology.
Keywords:
complexity, self-organization, order parameter, living systems, quasi-attractor.
complexity, self-organization, order parameter, living systems, quasi-attractor.
Введение. С позиций современной биофизики при описании физических, технических, химических систем и процессов в рамках детерминизма мы используем функциональные зависимости, что для биосистем эквивалентно заданию вектора состояния этих
