Bogdanov–Takens bifurcation in a predator–prey model with age structure

Zeitschrift für angewandte Mathematik und Physik volume 72, Article number: 4 (2021) Cite this article

Abstract

The results obtained in this article aim at analyzing Bogdanov–Takens bifurcation in a predator–prey model with an age structure for the predator. Firstly, we give the existence result of the Bogdanov–Takens singularity. Then we describe the bifurcation behavior of the parameterized predator–prey model with Bogdanov–Takens singularity.

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Author information

Affiliations

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

    Zhihua Liu

  2. Univ. Bordeaux, IMB, UMR 5251, 33400, Talence, France

    Pierre Magal

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

    Pierre Magal

Authors
  1. Zhihua Liu
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  2. Pierre Magal
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Correspondence to Pierre Magal.

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Research was partially supported by National Natural Science Foundation of China (Grant Nos. 11871007 and 11811530272) and the Fundamental Research Funds for the Central Universities.

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Liu, Z., Magal, P. Bogdanov–Takens bifurcation in a predator–prey model with age structure. Z. Angew. Math. Phys. 72, 4 (2021). https://doi.org/10.1007/s00033-020-01434-1

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Keywords

  • Non-densely defined Cauchy problems
  • Normal form
  • Bogdanov–Takens bifurcation
  • Homoclinic orbit
  • Hopf bifurcation
  • Predator–prey model
  • Age structure

Mathematics Subject Classification

  • 34K18
  • 37L10
  • 37L15
  • 35K90
  • 37G10
  • 92D25