Approximate Methods for Solving Problems of Mathematical Physics on Neural Hopfield Networks

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Approximate Methods for Solving Problems of Mathematical Physics on Neural Hopfield Networks. / Boykov, Ilya; Roudnev, Vladimir; Boykova, Alla.

In: Mathematics, Vol. 10, No. 13, 2207, 24.06.2022.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{7e23a86939fa4592965467cdc97a2bd5,

title = "Approximate Methods for Solving Problems of Mathematical Physics on Neural Hopfield Networks",

abstract = "A Hopfield neural network is described by a system of nonlinear ordinary differential equations. We develop a broad range of numerical schemes that are applicable for a wide range of computational problems. We review here our study on an approximate solution of the Fredholm integral equation, and linear and nonlinear singular and hypersingular integral equations, using a continuous method for solving operator equations. This method assumes that the original system is associated with a Cauchy problem for systems of ordinary differential equations on Hopfield neural networks. We present sufficient conditions for the Hopfield networks{\textquoteright} stability defined via coefficients of systems of differential equations.",

keywords = "Cauchy problem, continuous method, Hopfield neural network, hypersingular integral equations, nonlinear differential equations, singular, stability",

author = "Ilya Boykov and Vladimir Roudnev and Alla Boykova",

year = "2022",

month = jun,

day = "24",

doi = "10.3390/math10132207",

language = "English",

volume = "10",

journal = "Mathematics",

issn = "2227-7390",

publisher = "MDPI AG",

number = "13",

}

RIS

TY - JOUR

T1 - Approximate Methods for Solving Problems of Mathematical Physics on Neural Hopfield Networks

AU - Boykov, Ilya

AU - Roudnev, Vladimir

AU - Boykova, Alla

PY - 2022/6/24

Y1 - 2022/6/24

N2 - A Hopfield neural network is described by a system of nonlinear ordinary differential equations. We develop a broad range of numerical schemes that are applicable for a wide range of computational problems. We review here our study on an approximate solution of the Fredholm integral equation, and linear and nonlinear singular and hypersingular integral equations, using a continuous method for solving operator equations. This method assumes that the original system is associated with a Cauchy problem for systems of ordinary differential equations on Hopfield neural networks. We present sufficient conditions for the Hopfield networks’ stability defined via coefficients of systems of differential equations.

AB - A Hopfield neural network is described by a system of nonlinear ordinary differential equations. We develop a broad range of numerical schemes that are applicable for a wide range of computational problems. We review here our study on an approximate solution of the Fredholm integral equation, and linear and nonlinear singular and hypersingular integral equations, using a continuous method for solving operator equations. This method assumes that the original system is associated with a Cauchy problem for systems of ordinary differential equations on Hopfield neural networks. We present sufficient conditions for the Hopfield networks’ stability defined via coefficients of systems of differential equations.

KW - Cauchy problem

KW - continuous method

KW - Hopfield neural network

KW - hypersingular integral equations

KW - nonlinear differential equations

KW - singular

KW - stability

UR - http://www.scopus.com/inward/record.url?scp=85133278087&partnerID=8YFLogxK

U2 - 10.3390/math10132207

DO - 10.3390/math10132207

M3 - Article

AN - SCOPUS:85133278087

VL - 10

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 13

M1 - 2207

ER -

ID: 101703804