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

Русанов, В. А.; Daneev, A. V.; Linke, Yu. É.; Plesnyov, P.A.

doi:10.37622/adsa/15.2.2020.199-215

Cited by 2 publications

(1 citation statement)

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“…Methodologically, this problem can be interpreted as an adaptive adjustment of the structure of the polylinear components of equation ( 2), which is attractive in Dmodeling of nonlinear neurodynamic processes [18,19]; in this context, see Examples 14 [20].…”

Section: Discussionmentioning

confidence: 99%

An Inverse Problems for Nonlinear Evolution Equations: Criteria of Existence of an Invariant Polylinear Controller for a Second-Order Differential System in a Hilbert Space

Русанов¹,

Daneev²,

Lakeyev³

et al. 2021

International Journal of Difference Equations

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The solvability of the problem of realizing operator functions of an invariant polylinear controller (IPL-controller) of a non-stationary differential system (D-system) of the second order, which allows for two bundles of dynamic processes of the "trajectory, control" type that are induced in this D-system by two different polylinear controllers, to unite these bundles, through the action of the IPL-controller, into a subfamily of admissible solutions of the given Dsystem. The problem under consideration belongs to the type of nonstationary coefficient-operator inverse problems for evolution equations, including hyperbolic ones, in a separable Hilbert space and is solved on the basis of a qualitative study of the properties of continuity and semiadditivity of the RayleighRitz functional operator. The results obtained have applications in the theory of nonlinear infinite-dimensional adaptive dynamical systems for a class of higher-order polylinear differential models.

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Section: Discussionmentioning

confidence: 99%