Oscillation of Nicholson’s blowflies equation

Jaber, Ghofran Hassan; Mohamad, Hussain Ali

doi:10.47974/JIM-2304

Open Access Research Article

Oscillation of Nicholson’s blowflies equation

^*Ghofran Hassan JaberCorresponding authorghofran.radi2203m@csw.uobaghdad.edu.iqDepartment of MathematicsCollege of Science for WomenUniversity of BaghdadBaghdad, IraqView full profile → , Hussain Ali Mohamadhussainam_math@csw.uobaghdad.edu.iqDepartment of MathematicsCollege of Science for WomenUniversity of BaghdadBaghdad, IraqView full profile →

* Corresponding author · click or hover a name for details

pp. 1219–1227Vol. 29Issue 5-AMay 2026DOI: 10.47974/JIM-2304XML

Received:: 01 May 2025
Published Online:: 27 Jun 2026
Article type:: Research Article
Language:: EN
Article no.:: JIM-2304
Pages:: 1219–1227

Abstract

In this paper, the oscillation property and the asymptotic behavior of all solutions to Nicholson’s blowfly equation for variable-coefficient flies are studied. While most researchers have studied Nicholson’s blowfly equation, with constant coefficients, and established some conditions to ensure the oscillation of all solutions of this equation about the equilibrium. In this research, the Nicholson’s blowfly equation with variable coefficients was studied. By choosing the variable coefficient, we will have more than one equilibrium axis. This requires choosing points within the range of δ(ω) and P(ω) functions that are consistent with the axis of optimal equilibrium. Sufficient conditions are established to ensure that these solutions oscillate about the equilibrium axis. To obtain these conditions, some auxiliary Lemmas are presented, and their effectiveness in obtaining the main results is demonstrated. Examples of the obtained results are also presented, and illustrate how to choose the optimal equilibrium as well as the optimal points of δ(ω) and P(ω) which achieves oscillation of all solutions.

Keywords

Oscillation Nicholson’s blowflies’ model Nonlinear delay differential equations Asymptotic behavior

Subject Classifications

Primary 93A30Secondary 49K15

References

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