Bogdanov–Takens bifurcation in a predator–prey modelReport as inadecuate

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Zeitschrift für angewandte Mathematik und Physik

, 67:137

First Online: 19 October 2016Received: 30 July 2014Revised: 23 November 2015


In this paper, we investigate a class of predator–prey model with age structure and discuss whether the model can undergo Bogdanov–Takens bifurcation. The analysis is based on the normal form theory and the center manifold theory for semilinear equations with non-dense domain combined with integrated semigroup theory. Qualitative analysis indicates that there exist some parameter values such that this predator–prey model has an unique positive equilibrium which is Bogdanov–Takens singularity. Moreover, it is shown that under suitable small perturbation, the system undergoes the Bogdanov–Takens bifurcation in a small neighborhood of this positive equilibrium.

KeywordsPredator–prey model Age structure Normal forms Non-densely defined Bogdanov–Takens bifurcation Research was partially supported by NSFC Nos. 11471044 and 11371058, the Fundamental Research Funds for the Central Universities and Laboratory of Mathematics and Complex Systems, Ministry of Education.

Research was partially supported by the French Ministry of Foreign and European Affairs program France China PFCC Campus France 20932UL.

Research was partially supported by NSFC Nos. 11371248 and 11431008.

Mathematics Subject Classification34K18 37L10 37L15 35K90 37G10 92D25  Download to read the full article text

Author: Zhihua Liu - Pierre Magal - Dongmei Xiao


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