Existence of a Bilinear Delay Differential Realization of Nonlinear Neurodynamic Process in the Constructions of Entropic Rayleigh Ritz Operator

On the basis of tensor production of the real Hilbert spaces, functionalgeometric conditions (necessary and sufficient) are given for the existence of a differential realization model for experimental data of an "inputoutput" type describing the dynamic behavior of the "black box" in the class of controllable bilinear nonstationary ordinary differential equations of the second order with delay (including non-autonomous quasi-linear hyperbolic models) in the separable Hilbert space. Incidentally, the topological-metric conditions of continuity of the projectivization of the entropic RayleighRitz operator are substantiated with calculating the fundamental group of its image. The results obtained give incentives to develop a qualitative theory of non-linear structural identification of polylinear non-autonomous differential systems of higher orders with delay, as the tools of mathematical modeling for the weaklystructured neurodynamic processes.