On a general nonlinear problem with distributed delays

N. Tatar

doi:10.3103/S1068362317040045

On a general nonlinear problem with distributed delays

N. Tatar^*

^*Corresponding author for this work

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

4 Scopus citations

Abstract

The paper considers a general system of ordinary differential equations appearing in the neural network theory. The activation functions are assumed to be continuous and bounded by power type functions of the states and distributed delay terms. These activation functions are not necessarily Lipschitz continuous as it is commonly assumed in the literature. We obtain sufficient conditions for exponential decay of solutions.

Original language	English
Pages (from-to)	184-190
Number of pages	7
Journal	Journal of Contemporary Mathematical Analysis
Volume	52
Issue number	4
DOIs	https://doi.org/10.3103/S1068362317040045
State	Published - 1 Jul 2017

Bibliographical note

Publisher Copyright:
© 2017, Allerton Press, Inc.

Keywords

Neural network
activation function
distributed delay
exponential stabilization

ASJC Scopus subject areas

Analysis
Control and Optimization
Applied Mathematics

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10.3103/S1068362317040045

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title = "On a general nonlinear problem with distributed delays",

abstract = "The paper considers a general system of ordinary differential equations appearing in the neural network theory. The activation functions are assumed to be continuous and bounded by power type functions of the states and distributed delay terms. These activation functions are not necessarily Lipschitz continuous as it is commonly assumed in the literature. We obtain sufficient conditions for exponential decay of solutions.",

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N2 - The paper considers a general system of ordinary differential equations appearing in the neural network theory. The activation functions are assumed to be continuous and bounded by power type functions of the states and distributed delay terms. These activation functions are not necessarily Lipschitz continuous as it is commonly assumed in the literature. We obtain sufficient conditions for exponential decay of solutions.

AB - The paper considers a general system of ordinary differential equations appearing in the neural network theory. The activation functions are assumed to be continuous and bounded by power type functions of the states and distributed delay terms. These activation functions are not necessarily Lipschitz continuous as it is commonly assumed in the literature. We obtain sufficient conditions for exponential decay of solutions.

KW - Neural network

KW - activation function

KW - distributed delay

KW - exponential stabilization

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DO - 10.3103/S1068362317040045

M3 - Article

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JO - Journal of Contemporary Mathematical Analysis

JF - Journal of Contemporary Mathematical Analysis

IS - 4

ER -

On a general nonlinear problem with distributed delays

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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Cite this