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Normal Forms for an Age Structured Model

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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’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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Acknowledgments

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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Authors and Affiliations

  1. Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, 100083, People’s Republic of China

    Jixun Chu

  2. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, People’s Republic of China

    Zhihua Liu

  3. Université de Bordeaux, IMB, UMR 5251, 33400, Talence, France

    Pierre Magal

  4. CNRS, IMB, UMR 5251, 33400, Talence, France

    Pierre Magal

  5. Department of Mathematics, University of Miami, Coral Gables, FL, 33146, USA

    Shigui Ruan

Authors
  1. Jixun Chu
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  2. Zhihua Liu
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  3. Pierre Magal
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  4. Shigui Ruan
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Corresponding author

Correspondence to Shigui Ruan.

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Dedicated to Professor John Mallet-Paret on the occasion of his 60th birthday.

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Chu, J., Liu, Z., Magal, P. et al. Normal Forms for an Age Structured Model. J Dyn Diff Equat 28, 733–761 (2016). https://doi.org/10.1007/s10884-015-9500-8

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  • DOI: https://doi.org/10.1007/s10884-015-9500-8

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