On stability of delay equations with positive and negative coefficients with applications

Leonid Berezansky; Elena Braverman

doi:10.4171/ZAA/1633

On stability of delay equations with positive and negative coefficients with applications

Leonid Berezansky, Elena Braverman

Department of Mathematics

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

7 Scopus citations

Abstract

We obtain new explicit exponential stability conditions for linear scalar equations with positive and negative delayed terms m l x (t) + X a_k(t)x(h_k(t)) − ^X b_k(t)x(g_k(t)) = 0 k=1 k=1 and its modifications, and apply them to investigate local stability of Mackey–Glass type models x (t) = r(t) β _{1 +} ^x(_x ^g _n ((^t _g)) (t)) − γx(h(t)) and x (t) = r(t) β _{1 +} ^x _x (^g _n ((^t _h)) (t)) − γx(t).

Original language	English
Pages (from-to)	157-189
Number of pages	33
Journal	Zeitschrift für Analysis und ihre Anwendungen
Volume	38
Issue number	2
DOIs	https://doi.org/10.4171/ZAA/1633
State	Published - 1 Jan 2019

Keywords

Exponential stability
Local stability
Mackey–Glass equation
Positive and negative coefficients
Solution estimates
Variable and distributed delays

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.4171/ZAA/1633

Cite this

@article{4108a5fa4a2249b883be897cedfa87f3,

title = "On stability of delay equations with positive and negative coefficients with applications",

abstract = "We obtain new explicit exponential stability conditions for linear scalar equations with positive and negative delayed terms m l x (t) + X ak(t)x(hk(t)) − X bk(t)x(gk(t)) = 0 k=1 k=1 and its modifications, and apply them to investigate local stability of Mackey–Glass type models x (t) = r(t) β 1 + x(x g n ((t g)) (t)) − γx(h(t)) and x (t) = r(t) β 1 + x x (g n ((t h)) (t)) − γx(t).",

keywords = "Exponential stability, Local stability, Mackey–Glass equation, Positive and negative coefficients, Solution estimates, Variable and distributed delays",

author = "Leonid Berezansky and Elena Braverman",

note = "Publisher Copyright: {\textcopyright} European Mathematical Society.",

year = "2019",

month = jan,

day = "1",

doi = "10.4171/ZAA/1633",

language = "English",

volume = "38",

pages = "157--189",

journal = "Zeitschrift f{\"u}r Analysis und ihre Anwendungen",

issn = "0232-2064",

publisher = "Heldermann Verlag",

number = "2",

}

TY - JOUR

T1 - On stability of delay equations with positive and negative coefficients with applications

AU - Berezansky, Leonid

AU - Braverman, Elena

N1 - Publisher Copyright: © European Mathematical Society.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - We obtain new explicit exponential stability conditions for linear scalar equations with positive and negative delayed terms m l x (t) + X ak(t)x(hk(t)) − X bk(t)x(gk(t)) = 0 k=1 k=1 and its modifications, and apply them to investigate local stability of Mackey–Glass type models x (t) = r(t) β 1 + x(x g n ((t g)) (t)) − γx(h(t)) and x (t) = r(t) β 1 + x x (g n ((t h)) (t)) − γx(t).

AB - We obtain new explicit exponential stability conditions for linear scalar equations with positive and negative delayed terms m l x (t) + X ak(t)x(hk(t)) − X bk(t)x(gk(t)) = 0 k=1 k=1 and its modifications, and apply them to investigate local stability of Mackey–Glass type models x (t) = r(t) β 1 + x(x g n ((t g)) (t)) − γx(h(t)) and x (t) = r(t) β 1 + x x (g n ((t h)) (t)) − γx(t).

KW - Exponential stability

KW - Local stability

KW - Mackey–Glass equation

KW - Positive and negative coefficients

KW - Solution estimates

KW - Variable and distributed delays

UR - http://www.scopus.com/inward/record.url?scp=85069705093&partnerID=8YFLogxK

U2 - 10.4171/ZAA/1633

DO - 10.4171/ZAA/1633

M3 - Article

AN - SCOPUS:85069705093

SN - 0232-2064

VL - 38

SP - 157

EP - 189

JO - Zeitschrift für Analysis und ihre Anwendungen

JF - Zeitschrift für Analysis und ihre Anwendungen

IS - 2

ER -

On stability of delay equations with positive and negative coefficients with applications

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this