PERIODIC SOLUTIONS OF A HYPERBOLIC REACTION-DIFFUSION NICHOLSON’S BLOWFLIES EQUATION

Yujing Li; Ben Niu

doi:10.3934/dcdsb.2025068

PERIODIC SOLUTIONS OF A HYPERBOLIC REACTION-DIFFUSION NICHOLSON’S BLOWFLIES EQUATION

Yujing Li
, Ben Niu^*

^*Corresponding author for this work

Harbin Institute of Technology Weihai

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

Abstract

In this paper, we investigate Nicholson’s blowflies equation with advection and inertia, which is a type of hyperbolic equation. By analyzing the distribution of the eigenvalues, linear stability and the conditions ensuring the existence of periodic solutions are obtained. We first transform the hyperbolic equation into a system of partial integral equations. Then, applying the Lyapunov-Schmidt reduction method and a generalized implicit function theorem, we obtain the existence of periodic solutions by analyzing the bifurcation equation. In the end, numerical results are performed to illustrate the effect of the inertial and advection terms.

Original language	English
Pages (from-to)	4583-4610
Number of pages	28
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	30
Issue number	12
DOIs	https://doi.org/10.3934/dcdsb.2025068
State	Published - Dec 2025
Externally published	Yes

Keywords

Lyapunov-Schmidt reduction
Nicholson’s blowflies equation
hyperbolic equations
inertia term
periodic solution

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10.3934/dcdsb.2025068

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title = "PERIODIC SOLUTIONS OF A HYPERBOLIC REACTION-DIFFUSION NICHOLSON{\textquoteright}S BLOWFLIES EQUATION",

abstract = "In this paper, we investigate Nicholson{\textquoteright}s blowflies equation with advection and inertia, which is a type of hyperbolic equation. By analyzing the distribution of the eigenvalues, linear stability and the conditions ensuring the existence of periodic solutions are obtained. We first transform the hyperbolic equation into a system of partial integral equations. Then, applying the Lyapunov-Schmidt reduction method and a generalized implicit function theorem, we obtain the existence of periodic solutions by analyzing the bifurcation equation. In the end, numerical results are performed to illustrate the effect of the inertial and advection terms.",

keywords = "Lyapunov-Schmidt reduction, Nicholson{\textquoteright}s blowflies equation, hyperbolic equations, inertia term, periodic solution",

author = "Yujing Li and Ben Niu",

year = "2025",

month = dec,

doi = "10.3934/dcdsb.2025068",

language = "英语",

volume = "30",

pages = "4583--4610",

journal = "Discrete and Continuous Dynamical Systems - Series B",

issn = "1531-3492",

publisher = "American Institute of Mathematical Sciences",

number = "12",

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T1 - PERIODIC SOLUTIONS OF A HYPERBOLIC REACTION-DIFFUSION NICHOLSON’S BLOWFLIES EQUATION

AU - Li, Yujing

AU - Niu, Ben

PY - 2025/12

Y1 - 2025/12

N2 - In this paper, we investigate Nicholson’s blowflies equation with advection and inertia, which is a type of hyperbolic equation. By analyzing the distribution of the eigenvalues, linear stability and the conditions ensuring the existence of periodic solutions are obtained. We first transform the hyperbolic equation into a system of partial integral equations. Then, applying the Lyapunov-Schmidt reduction method and a generalized implicit function theorem, we obtain the existence of periodic solutions by analyzing the bifurcation equation. In the end, numerical results are performed to illustrate the effect of the inertial and advection terms.

AB - In this paper, we investigate Nicholson’s blowflies equation with advection and inertia, which is a type of hyperbolic equation. By analyzing the distribution of the eigenvalues, linear stability and the conditions ensuring the existence of periodic solutions are obtained. We first transform the hyperbolic equation into a system of partial integral equations. Then, applying the Lyapunov-Schmidt reduction method and a generalized implicit function theorem, we obtain the existence of periodic solutions by analyzing the bifurcation equation. In the end, numerical results are performed to illustrate the effect of the inertial and advection terms.

KW - Lyapunov-Schmidt reduction

KW - Nicholson’s blowflies equation

KW - hyperbolic equations

KW - inertia term

KW - periodic solution

UR - https://www.scopus.com/pages/publications/105009459734

U2 - 10.3934/dcdsb.2025068

DO - 10.3934/dcdsb.2025068

M3 - 文章

AN - SCOPUS:105009459734

SN - 1531-3492

VL - 30

SP - 4583

EP - 4610

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

IS - 12

ER -

PERIODIC SOLUTIONS OF A HYPERBOLIC REACTION-DIFFUSION NICHOLSON’S BLOWFLIES EQUATION

Abstract

Keywords

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