Nonresonant periodic perturbation of the hopf bifurcation

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3 Citations (Scopus)

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

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Hopf bifurcation
Autonomous Systems
Hopf Bifurcation
Periodic Solution
Perturbation
Integral Manifolds
Perturbed System
Curve
Text

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Nonresonant periodic perturbation of the hopf bifurcation. / Smith, Hal.

In: Applicable Analysis, Vol. 12, No. 3, 01.01.1981, p. 173-195.

Research output: Contribution to journalArticle

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