Formalization of the effect of “repetition without repetition” discovered by N.A. Bernshtein

Abstract

No adequate models for the effect of “repetition without repetition,” as discovered by N.A. Bernshtein in 1947, have been developed. This problem goes beyond the scope of the biomechanics and biophysics of movement and applies to all homeostatic systems. Its essence lies in the absence of both stationary modes (dx/dt = 0) and stable distribution functions f(x_i) (obtained by sequential registration of samples) for any component x_i of the state vector of a complex biological system x(t) = (x₁, x₂, …, x_m)^T: that is, x_i do not coincide! Simple models of such homeostatic systems represented as pairwise comparison matrices for the samples are proposed; these models can characterize a specific type of chaos that exists in biological systems. This chaos is different from deterministic chaos and is currently being tested as an approach for the description of complex biological systems (complexity).