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Existence of a bilinear delay differential realization of nonlinear neurodynamic process in the constructions of entropic Rayleigh-Ritz operator

Авторы: Rusanov V.A., Daneev A.V., Linke Yu.É., Plesnyov P.A.

Журнал: Advances in Dynamical Systems and Applications

Том: 15

Номер: 2

Год: 2020

Отчётный год: 2020

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DOI: 10.37622/ADSA/15.2.2020.199-215

Аннотация: 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.

Индексируется WOS: Нет

Индексируется Scopus: Нет

Индексируется УБС: Нет

Индексируется РИНЦ: Нет

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Индексируется CORE: Нет

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