The necessity of the Hopf bifurcation for periodically forced oscillators

B. B. Peckham

Research output: Contribution to journalArticlepeer-review

25 Scopus citations

Abstract

By varying the forcing frequency and amplitude of a periodically forced planar oscillator, the author obtains a rich variety of responses. Whenever the resonance regions that are known to exist for small amplitudes of forcing terminate, he shows that a fixed-point Hopf bifurcation must be involved. The main tool, whose properties he discusses in detail, is a self-rotation number for orbits in the plane. He illustrates his theorems with a numerical model.

Original languageEnglish (US)
Pages (from-to)261-280
Number of pages20
JournalNonlinearity
Volume3
Issue number2
DOIs
StatePublished - May 1990

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