Abstract:

As is known, stationary modes of natural complex systems (or biosystems) are described by the condition, namely: dx/dt=0, xi = const for the state vector of any system x=x(t)=(x1, x2, ..., xm)T in the m-dimensional phase state space. Typically, for biosystems, the criterion of the invariance of statistical functions f(xi) or the invariance of their statistical characteristics (dispersions, mathematical expectations, spectral signal densities, autocorrelation A (t), etc.) is used. However, over the past 20-25 years it has been proved that complex (homeostatic) biosystems do not meet the condition dx/dt = 0. At the same time, they do not preserve f(xi), A(t), spectral densities, etc. These are systems that cannot be described in terms of functional analysis or stochastics. They demonstrate the lack of statistical stability of any recorded samples of the components xi(t) for their states (initial x0(t), intermediate xi(t), and final state xk(t)). Therefore, these systems are not an object of modern deterministic and stochastic science. The article proposes new methods and models for describing any homeostatic system in an unchanged (single) homeostatic state based on the parameters of quasi-attractors and matrices of pairwise comparisons of samples xi(t). It is noted that meteorological parameters and climate have homeostatic properties, for the description of which systems of differential equations with a discontinuous right-hand side are proposed.

Keywords: homeostatic systems, stationary mode, pseudoattractor, differential equations, Eskov-Zinchenko effects