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arXiv · 2105.07478

A short proof for Hopf bifurcation in Gurtin-MacCamy's population dynamics model

Arnaud Ducrot·Hao Kang·Pierre Magal
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Abstract

In this paper, we provide a short proof for the Hopf bifurcation theorem in the Gurtin-MacCamy's population dynamics model. Here we use the Crandall and Rabinowitz's approach, based on the implicit function theorem. Compared with previous methods, here we require the age-specific birth rate to be slightly smoother (roughly of bounded variation), but we have a huge gain for the length of the proof.

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Arnaud Ducrot, Hao Kang, Pierre Magal. 2021-05-16. A short proof for Hopf bifurcation in Gurtin-MacCamy's population dynamics model. https://arxiv.org/abs/2105.07478

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