A new stability test for linear neutral differential equations

Leonid Berezansky; Elena Braverman

doi:10.1016/j.aml.2018.02.005

A new stability test for linear neutral differential equations

Leonid Berezansky, Elena Braverman

Department of Mathematics

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

3 Scopus citations

Abstract

We obtain new explicit exponential stability conditions for the linear scalar neutral equation with two bounded delays ẋ(t)−a(t)ẋ(g(t))+b(t)x(h(t))=0, where 0≤a(t)≤A₀<1, 0<b₀≤b(t)≤B, using the Bohl–Perron theorem and a transformation of the neutral equation into a differential equation with an infinite number of delays. The results are applied to the neutral logistic equation.

Original language	English
Pages (from-to)	79-85
Number of pages	7
Journal	Applied Mathematics Letters
Volume	81
DOIs	https://doi.org/10.1016/j.aml.2018.02.005
State	Published - 1 Jul 2018

Keywords

Bohl–Perron theorem
Explicit stability conditions
Logistic neutral differential equation
Neutral equations
Uniform exponential stability
Variable delays

ASJC Scopus subject areas

Applied Mathematics

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10.1016/j.aml.2018.02.005

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title = "A new stability test for linear neutral differential equations",

abstract = "We obtain new explicit exponential stability conditions for the linear scalar neutral equation with two bounded delays ẋ(t)−a(t)ẋ(g(t))+b(t)x(h(t))=0, where 0≤a(t)≤A0<1, 00≤b(t)≤B, using the Bohl–Perron theorem and a transformation of the neutral equation into a differential equation with an infinite number of delays. The results are applied to the neutral logistic equation.",

keywords = "Bohl–Perron theorem, Explicit stability conditions, Logistic neutral differential equation, Neutral equations, Uniform exponential stability, Variable delays",

author = "Leonid Berezansky and Elena Braverman",

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AU - Braverman, Elena

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N2 - We obtain new explicit exponential stability conditions for the linear scalar neutral equation with two bounded delays ẋ(t)−a(t)ẋ(g(t))+b(t)x(h(t))=0, where 0≤a(t)≤A0<1, 00≤b(t)≤B, using the Bohl–Perron theorem and a transformation of the neutral equation into a differential equation with an infinite number of delays. The results are applied to the neutral logistic equation.

AB - We obtain new explicit exponential stability conditions for the linear scalar neutral equation with two bounded delays ẋ(t)−a(t)ẋ(g(t))+b(t)x(h(t))=0, where 0≤a(t)≤A0<1, 00≤b(t)≤B, using the Bohl–Perron theorem and a transformation of the neutral equation into a differential equation with an infinite number of delays. The results are applied to the neutral logistic equation.

KW - Bohl–Perron theorem

KW - Explicit stability conditions

KW - Logistic neutral differential equation

KW - Neutral equations

KW - Uniform exponential stability

KW - Variable delays

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JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

ER -

A new stability test for linear neutral differential equations

Abstract

Keywords

ASJC Scopus subject areas

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