Nonresonant periodic perturbation of the hopf bifurcation

Hal Smith

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

In this paper the following periodically perturbed autonomous system text omatted in which g is 2π/ω-periodic in t and f(0,η) = 0 is considered. It is assumed that the autonomous system obtained by setting b=0 undergoes a generic Hopf bifurcation from x = 0 at η= 0 and that the frequency,ω, is not in resonance with the frequency of the Hopf periodic solution. Under these conditions, we show that an integral manifold of solutions bifurcates from the unique 2π/ω-periodic solution, x*, of (1) on one side of the neutral stability curve for x* in the (b,η) plane.

Original languageEnglish (US)
Pages (from-to)173-195
Number of pages23
JournalApplicable Analysis
Volume12
Issue number3
DOIs
StatePublished - Jan 1 1981

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Nonresonant periodic perturbation of the hopf bifurcation'. Together they form a unique fingerprint.

Cite this