HopfBifurcationsHopf bifurcation

Andrew Fowler () and Mark McGuinness
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Andrew Fowler: University of Limerick, MACSI
Mark McGuinness: Victoria University of Wellington, School of Mathematics and Statistics

Chapter Chapter 3 in Chaos, 2019, pp 49-98 from Springer

Abstract: Abstract The Hopf bifurcation theorem is proved in the roundabout way adopted in Hassard, Kazarinoff and Wan’s 1981 book, proceeding by way of normal form theory and the centre manifold theorem before the final proof using the implicit function theorem. There is then a thorough discussion of secondary Hopf bifurcation, leading to the ideas of Arnold tongues and frequency locking, and the concept of tertiary Hopf bifurcation is briefly raised and dismissed.

Date: 2019
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DOI: 10.1007/978-3-030-32538-1_3

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