A short proof for Hopf bifurcation in Gurtin-MacCamy's population dynamics model
Dynamical Systems
2021-05-18 v1 Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.2105.07478,
title = {A short proof for Hopf bifurcation in Gurtin-MacCamy's population dynamics model},
author = {Arnaud Ducrot and Hao Kang and Pierre Magal},
journal= {arXiv preprint arXiv:2105.07478},
year = {2021}
}