Homeostatic System Can Not Be Described by Stochastics or Deterministic Chaos

Abstract

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.