Oscillation and global attractivity in a periodic Nicholson's blowflies model

S. H. Saker, Shruti Agarwal

Research output: Contribution to journalArticle

Abstract

In this paper, we shall consider the nonlinear delay differential equation N′(t) = -δ(t)N(t) + P(t)N(t - mw)e-aN(t - mw), (*) where tn is a positive integer, δ(t) and P(t) are positive periodic functions of period w. In the nondelay case, we shall show that (*) has a unique positive periodic solution N̄(t), and provide sufficient conditions for the global attractivity of N̄(t). In the delay case, we shall present sufficient conditions for the oscillation of all positive solutions of (*) about N̄(t), and establish sufficient conditions for the global attractivity of N̄(t).

Original languageEnglish (US)
Pages (from-to)719-731
Number of pages13
JournalMathematical and Computer Modelling
Volume35
Issue number7-8
DOIs
StatePublished - Mar 26 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
  • Nicholson's blowflies model
  • Nonlinear delay differential equations
  • Oscillation

ASJC Scopus subject areas

  • Modeling and Simulation
  • Computer Science Applications

Cite this

Oscillation and global attractivity in a periodic Nicholson's blowflies model. / Saker, S. H.; Agarwal, Shruti.

In: Mathematical and Computer Modelling, Vol. 35, No. 7-8, 26.03.2002, p. 719-731.

Research output: Contribution to journalArticle

@article{740521921a5245eabcfcdb3303a87d2d,
title = "Oscillation and global attractivity in a periodic Nicholson's blowflies model",
abstract = "In this paper, we shall consider the nonlinear delay differential equation N′(t) = -δ(t)N(t) + P(t)N(t - mw)e-aN(t - mw), (*) where tn is a positive integer, δ(t) and P(t) are positive periodic functions of period w. In the nondelay case, we shall show that (*) has a unique positive periodic solution N̄(t), and provide sufficient conditions for the global attractivity of N̄(t). In the delay case, we shall present sufficient conditions for the oscillation of all positive solutions of (*) about N̄(t), and establish sufficient conditions for the global attractivity of N̄(t).",
keywords = "Global attractivity, Nicholson's blowflies model, Nonlinear delay differential equations, Oscillation",
author = "Saker, {S. H.} and Shruti Agarwal",
year = "2002",
month = "3",
day = "26",
doi = "10.1016/S0895-7177(02)00043-2",
language = "English (US)",
volume = "35",
pages = "719--731",
journal = "Mathematical and Computer Modelling",
issn = "0895-7177",
publisher = "Elsevier Limited",
number = "7-8",

}

TY - JOUR

T1 - Oscillation and global attractivity in a periodic Nicholson's blowflies model

AU - Saker, S. H.

AU - Agarwal, Shruti

PY - 2002/3/26

Y1 - 2002/3/26

N2 - In this paper, we shall consider the nonlinear delay differential equation N′(t) = -δ(t)N(t) + P(t)N(t - mw)e-aN(t - mw), (*) where tn is a positive integer, δ(t) and P(t) are positive periodic functions of period w. In the nondelay case, we shall show that (*) has a unique positive periodic solution N̄(t), and provide sufficient conditions for the global attractivity of N̄(t). In the delay case, we shall present sufficient conditions for the oscillation of all positive solutions of (*) about N̄(t), and establish sufficient conditions for the global attractivity of N̄(t).

AB - In this paper, we shall consider the nonlinear delay differential equation N′(t) = -δ(t)N(t) + P(t)N(t - mw)e-aN(t - mw), (*) where tn is a positive integer, δ(t) and P(t) are positive periodic functions of period w. In the nondelay case, we shall show that (*) has a unique positive periodic solution N̄(t), and provide sufficient conditions for the global attractivity of N̄(t). In the delay case, we shall present sufficient conditions for the oscillation of all positive solutions of (*) about N̄(t), and establish sufficient conditions for the global attractivity of N̄(t).

KW - Global attractivity

KW - Nicholson's blowflies model

KW - Nonlinear delay differential equations

KW - Oscillation

UR - http://www.scopus.com/inward/record.url?scp=0037177280&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037177280&partnerID=8YFLogxK

U2 - 10.1016/S0895-7177(02)00043-2

DO - 10.1016/S0895-7177(02)00043-2

M3 - Article

VL - 35

SP - 719

EP - 731

JO - Mathematical and Computer Modelling

JF - Mathematical and Computer Modelling

SN - 0895-7177

IS - 7-8

ER -