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

Ducrot, Arnaud; Kang, Hao; Magal, Pierre

doi:10.1090/proc/15892

A short proof for Hopf bifurcation in Gurtin-MacCamy’s population dynamics model
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by Arnaud Ducrot, Hao Kang and Pierre Magal;

Proc. Amer. Math. Soc. 151 (2023), 3561-3575

DOI: https://doi.org/10.1090/proc/15892

Published electronically: April 28, 2023

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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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A short proof for Hopf bifurcation in Gurtin-MacCamy’s population dynamics model
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Abstract: