Bifurcation of synchronized periodic solutions in systems of coupled oscillators II: Global bifurcation in coupled planar oscillators

Masaji Watanabe

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We continue the study of a class of differential equations that govern the evolution of indirectly coupled oscillators. In a previous paper we established the existence of synchronized periodic solutions for weak and strong coupling. In this paper we present an example that shows an interesting behavior of the solutions for intermediate coupling strength. We analyze a two-parameter family of branches of periodic solutions and show when a branch has Hopf bifurcation points and/or turning points. We also study the stability of the periodic solutions.

Original languageEnglish
Pages (from-to)1527-1554
Number of pages28
JournalRocky Mountain Journal of Mathematics
Volume23
Issue number4
DOIs
Publication statusPublished - Sep 1993
Externally publishedYes

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Global Bifurcation
Coupled Oscillators
Periodic Solution
Bifurcation
Branch
Turning Point
Weak Coupling
Bifurcation Point
Strong Coupling
Hopf Bifurcation
Two Parameters
Continue
Differential equation

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Bifurcation of synchronized periodic solutions in systems of coupled oscillators II : Global bifurcation in coupled planar oscillators. / Watanabe, Masaji.

In: Rocky Mountain Journal of Mathematics, Vol. 23, No. 4, 09.1993, p. 1527-1554.

Research output: Contribution to journalArticle

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