Oscillation and global attractivity in a nonlinear delay periodic model of respiratory dynamics

S. H. Saker, Shruti Agarwal

Research output: Contribution to journalArticle

Abstract

In this paper, we shall consider the nonlinear delay differential equation x′ (t) + αV (t)x(t)xn (t - mω)/θn + xn (t - mω) = λ (t), where m and n are positive integers, and V (t) and λ(t) are positive periodic functions of period ω. In the nondelay case, we shall show that (*) has a unique positive periodic solution x̄(t) and provides sufficient conditions for the global attractivity of x̄(t). In the delay case, we shall present sufficient conditions for the oscillation of all positive solutions of (*) about x̄(t) and establish sufficient conditions for the global attractivity of x̄(t).

Original languageEnglish (US)
Pages (from-to)623-632
Number of pages10
JournalComputers and Mathematics with Applications
Volume44
Issue number5-6
DOIs
StatePublished - Sep 1 2002
Externally publishedYes

Fingerprint

Global Attractivity
Differential equations
Oscillation
Sufficient Conditions
Positive Periodic Solution
Periodic Functions
Delay Differential Equations
Nonlinear Differential Equations
Positive Solution
Model
Integer

Keywords

  • Global attractivity
  • Nonlinear delay differential equation
  • Oscillation
  • Respiratory dynamics

ASJC Scopus subject areas

  • Modeling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

Cite this

Oscillation and global attractivity in a nonlinear delay periodic model of respiratory dynamics. / Saker, S. H.; Agarwal, Shruti.

In: Computers and Mathematics with Applications, Vol. 44, No. 5-6, 01.09.2002, p. 623-632.

Research output: Contribution to journalArticle

@article{8a783c994f954c68807d357d97df2f87,
title = "Oscillation and global attractivity in a nonlinear delay periodic model of respiratory dynamics",
abstract = "In this paper, we shall consider the nonlinear delay differential equation x′ (t) + αV (t)x(t)xn (t - mω)/θn + xn (t - mω) = λ (t), where m and n are positive integers, and V (t) and λ(t) are positive periodic functions of period ω. In the nondelay case, we shall show that (*) has a unique positive periodic solution x̄(t) and provides sufficient conditions for the global attractivity of x̄(t). In the delay case, we shall present sufficient conditions for the oscillation of all positive solutions of (*) about x̄(t) and establish sufficient conditions for the global attractivity of x̄(t).",
keywords = "Global attractivity, Nonlinear delay differential equation, Oscillation, Respiratory dynamics",
author = "Saker, {S. H.} and Shruti Agarwal",
year = "2002",
month = "9",
day = "1",
doi = "10.1016/S0898-1221(02)00177-3",
language = "English (US)",
volume = "44",
pages = "623--632",
journal = "Computers and Mathematics with Applications",
issn = "0898-1221",
publisher = "Elsevier Limited",
number = "5-6",

}

TY - JOUR

T1 - Oscillation and global attractivity in a nonlinear delay periodic model of respiratory dynamics

AU - Saker, S. H.

AU - Agarwal, Shruti

PY - 2002/9/1

Y1 - 2002/9/1

N2 - In this paper, we shall consider the nonlinear delay differential equation x′ (t) + αV (t)x(t)xn (t - mω)/θn + xn (t - mω) = λ (t), where m and n are positive integers, and V (t) and λ(t) are positive periodic functions of period ω. In the nondelay case, we shall show that (*) has a unique positive periodic solution x̄(t) and provides sufficient conditions for the global attractivity of x̄(t). In the delay case, we shall present sufficient conditions for the oscillation of all positive solutions of (*) about x̄(t) and establish sufficient conditions for the global attractivity of x̄(t).

AB - In this paper, we shall consider the nonlinear delay differential equation x′ (t) + αV (t)x(t)xn (t - mω)/θn + xn (t - mω) = λ (t), where m and n are positive integers, and V (t) and λ(t) are positive periodic functions of period ω. In the nondelay case, we shall show that (*) has a unique positive periodic solution x̄(t) and provides sufficient conditions for the global attractivity of x̄(t). In the delay case, we shall present sufficient conditions for the oscillation of all positive solutions of (*) about x̄(t) and establish sufficient conditions for the global attractivity of x̄(t).

KW - Global attractivity

KW - Nonlinear delay differential equation

KW - Oscillation

KW - Respiratory dynamics

UR - http://www.scopus.com/inward/record.url?scp=0036725839&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036725839&partnerID=8YFLogxK

U2 - 10.1016/S0898-1221(02)00177-3

DO - 10.1016/S0898-1221(02)00177-3

M3 - Article

VL - 44

SP - 623

EP - 632

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

IS - 5-6

ER -