Journal of Dynamics and Differential Equations

, Volume 28, Issue 3–4, pp 733–761 | Cite as

Normal Forms for an Age Structured Model



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.


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

Mathematics Subject Classfication

34K15 34C20 37L10 58F36 



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).


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Jixun Chu
    • 1
  • Zhihua Liu
    • 2
  • Pierre Magal
    • 3
    • 4
  • Shigui Ruan
    • 5
  1. 1.Department of Applied Mathematics, School of Mathematics and PhysicsUniversity of Science and Technology BeijingBeijingPeople’s Republic of China
  2. 2.School of Mathematical SciencesBeijing Normal UniversityBeijingPeople’s Republic of China
  3. 3.Université de Bordeaux, IMB, UMR 5251TalenceFrance
  4. 4.CNRS, IMB, UMR 5251TalenceFrance
  5. 5.Department of MathematicsUniversity of MiamiCoral GablesUSA

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