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 › peer-review

10 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)
Pages (from-to)	733-761
Number of pages	29
Journal	Journal of Dynamics and Differential Equations
Volume	28
Issue number	3-4
DOIs	https://doi.org/10.1007/s10884-015-9500-8
State	Published - Sep 1 2016

Keywords

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

ASJC Scopus subject areas

Analysis

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10.1007/s10884-015-9500-8

Cite this

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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",

note = "Funding Information: Research of Jixun Chu was partially supported by NSFC (No. 11401021). Research of Zhihua Liu was partially supported by NSFC (Nos. 11471044 and 11371058). Research of Pierre Magal was partially supported by the French Ministry of Foreign and European Affairs program France-China PFCC EGIDE (20932UL). Research of Shigui Ruan was partially supported by NSF (DMS-1412454). Publisher Copyright: {\textcopyright} 2015, Springer Science+Business Media New York.",

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AU - Liu, Zhihua

AU - Magal, Pierre

AU - Ruan, Shigui

N1 - Funding Information: Research of Jixun Chu was partially supported by NSFC (No. 11401021). Research of Zhihua Liu was partially supported by NSFC (Nos. 11471044 and 11371058). Research of Pierre Magal was partially supported by the French Ministry of Foreign and European Affairs program France-China PFCC EGIDE (20932UL). Research of Shigui Ruan was partially supported by NSF (DMS-1412454). Publisher Copyright: © 2015, Springer Science+Business Media New York.

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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.

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KW - Hopf bifurcation

KW - Non-densely defined Cauchy problem

KW - Normal form

KW - Periodic solution

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Normal Forms for an Age Structured Model

Abstract

Keywords

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