Normal Forms for an Age Structured Model

Jixun Chu; Zhihua Liu; Pierre Magal; Shigui Ruan

doi:10.1007/s10884-015-9500-8

Normal Forms for an Age Structured Model

Jixun Chu, Zhihua Liu, Pierre Magal, Shigui Ruan

Mathematics

Research output: Contribution to journal › Article

9 Scopus citations

Abstract

In this paper, we apply the recently developed normal form theory for abstract Cauchy problems with non-dense domain in Liu et al. (J Diff Equ 257:921–1011, 2014) to study normal forms for an age structured model. We provide detailed computations for the Taylor’s expansion of the reduced system on the center manifold, from which explicit formulae are given to determine the direction of the Hopf bifurcation and the stability and amplitude of the bifurcating periodic solutions.

Original language	English (US)
Journal	Journal of Dynamics and Differential Equations
DOIs	https://doi.org/10.1007/s10884-015-9500-8
State	Accepted/In press - Oct 7 2015

Keywords

Age structured model
Hopf bifurcation
Non-densely defined Cauchy problem
Normal form
Periodic solution

ASJC Scopus subject areas

Analysis

Access to Document

10.1007/s10884-015-9500-8

Fingerprint Dive into the research topics of 'Normal Forms for an Age Structured Model'. Together they form a unique fingerprint.

Cite this

Chu, J., Liu, Z., Magal, P., & Ruan, S. (Accepted/In press). Normal Forms for an Age Structured Model. Journal of Dynamics and Differential Equations. https://doi.org/10.1007/s10884-015-9500-8

@article{cb3a0e05a65c421a89a90f95f9bb36af,

title = "Normal Forms for an Age Structured Model",

abstract = "In this paper, we apply the recently developed normal form theory for abstract Cauchy problems with non-dense domain in Liu et al. (J Diff Equ 257:921–1011, 2014) to study normal forms for an age structured model. We provide detailed computations for the Taylor{\textquoteright}s expansion of the reduced system on the center manifold, from which explicit formulae are given to determine the direction of the Hopf bifurcation and the stability and amplitude of the bifurcating periodic solutions.",

keywords = "Age structured model, Hopf bifurcation, Non-densely defined Cauchy problem, Normal form, Periodic solution",

author = "Jixun Chu and Zhihua Liu and Pierre Magal and Shigui Ruan",

year = "2015",

month = oct,

day = "7",

doi = "10.1007/s10884-015-9500-8",

language = "English (US)",

journal = "Journal of Dynamics and Differential Equations",

issn = "1040-7294",

publisher = "Springer New York",

}

TY - JOUR

T1 - Normal Forms for an Age Structured Model

AU - Chu, Jixun

AU - Liu, Zhihua

AU - Magal, Pierre

AU - Ruan, Shigui

PY - 2015/10/7

Y1 - 2015/10/7

N2 - In this paper, we apply the recently developed normal form theory for abstract Cauchy problems with non-dense domain in Liu et al. (J Diff Equ 257:921–1011, 2014) to study normal forms for an age structured model. We provide detailed computations for the Taylor’s expansion of the reduced system on the center manifold, from which explicit formulae are given to determine the direction of the Hopf bifurcation and the stability and amplitude of the bifurcating periodic solutions.

AB - In this paper, we apply the recently developed normal form theory for abstract Cauchy problems with non-dense domain in Liu et al. (J Diff Equ 257:921–1011, 2014) to study normal forms for an age structured model. We provide detailed computations for the Taylor’s expansion of the reduced system on the center manifold, from which explicit formulae are given to determine the direction of the Hopf bifurcation and the stability and amplitude of the bifurcating periodic solutions.

KW - Age structured model

KW - Hopf bifurcation

KW - Non-densely defined Cauchy problem

KW - Normal form

KW - Periodic solution

UR - http://www.scopus.com/inward/record.url?scp=84944699159&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84944699159&partnerID=8YFLogxK

U2 - 10.1007/s10884-015-9500-8

DO - 10.1007/s10884-015-9500-8

M3 - Article

AN - SCOPUS:84944699159

JO - Journal of Dynamics and Differential Equations

JF - Journal of Dynamics and Differential Equations

SN - 1040-7294

ER -