Stability conditions for scalar delay differential equations with a non-delay term

Leonid Berezansky; Elena Braverman

doi:10.1016/j.amc.2014.10.088

Stability conditions for scalar delay differential equations with a non-delay term

Leonid Berezansky, Elena Braverman

Department of Mathematics

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

5 Scopus citations

Abstract

The problem considered in the paper is exponential stability of linear equations and global attractivity of nonlinear non-autonomous equations which include a non-delay term and one or more delayed terms. First, we demonstrate that introducing a non-delay term with a non-negative coefficient can destroy stability of the delay equation. Next, sufficient exponential stability conditions for linear equations with concentrated or distributed delays and global attractivity conditions for nonlinear equations are obtained. The nonlinear results are applied to the Mackey-Glass model of respiratory dynamics.

Original language	English
Pages (from-to)	157-164
Number of pages	8
Journal	Applied Mathematics and Computation
Volume	250
DOIs	https://doi.org/10.1016/j.amc.2014.10.088
State	Published - 1 Jan 2015

Keywords

Global asymptotic stability
Linear and nonlinear delay differential equations
Mackey-Glass equation of respiratory dynamics

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2014.10.088

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title = "Stability conditions for scalar delay differential equations with a non-delay term",

abstract = "The problem considered in the paper is exponential stability of linear equations and global attractivity of nonlinear non-autonomous equations which include a non-delay term and one or more delayed terms. First, we demonstrate that introducing a non-delay term with a non-negative coefficient can destroy stability of the delay equation. Next, sufficient exponential stability conditions for linear equations with concentrated or distributed delays and global attractivity conditions for nonlinear equations are obtained. The nonlinear results are applied to the Mackey-Glass model of respiratory dynamics.",

keywords = "Global asymptotic stability, Linear and nonlinear delay differential equations, Mackey-Glass equation of respiratory dynamics",

author = "Leonid Berezansky and Elena Braverman",

note = "Funding Information: The first author was partially supported by Israeli Ministry of Absorption . The second author was partially supported by the NSERC Discovery Grant. Publisher Copyright: {\textcopyright} 2014 Elsevier Inc. All rights reserved.",

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AU - Berezansky, Leonid

AU - Braverman, Elena

N1 - Funding Information: The first author was partially supported by Israeli Ministry of Absorption . The second author was partially supported by the NSERC Discovery Grant. Publisher Copyright: © 2014 Elsevier Inc. All rights reserved.

PY - 2015/1/1

Y1 - 2015/1/1

N2 - The problem considered in the paper is exponential stability of linear equations and global attractivity of nonlinear non-autonomous equations which include a non-delay term and one or more delayed terms. First, we demonstrate that introducing a non-delay term with a non-negative coefficient can destroy stability of the delay equation. Next, sufficient exponential stability conditions for linear equations with concentrated or distributed delays and global attractivity conditions for nonlinear equations are obtained. The nonlinear results are applied to the Mackey-Glass model of respiratory dynamics.

AB - The problem considered in the paper is exponential stability of linear equations and global attractivity of nonlinear non-autonomous equations which include a non-delay term and one or more delayed terms. First, we demonstrate that introducing a non-delay term with a non-negative coefficient can destroy stability of the delay equation. Next, sufficient exponential stability conditions for linear equations with concentrated or distributed delays and global attractivity conditions for nonlinear equations are obtained. The nonlinear results are applied to the Mackey-Glass model of respiratory dynamics.

KW - Global asymptotic stability

KW - Linear and nonlinear delay differential equations

KW - Mackey-Glass equation of respiratory dynamics

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SN - 0096-3003

VL - 250

SP - 157

EP - 164

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

Stability conditions for scalar delay differential equations with a non-delay term

Abstract

Keywords

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