TRANSITIONS IN WEAKLY-COUPLED NONLINEAR OSCILLATORS.

Paul H. Steen*, Stephen H. Davis

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

Two oscillators having natural frequencies delta and gamma and damping coefficients proportional to minus lambda are weakly coupled through cubic nonlinearities. As lambda is increased through lambda //c EQUVLNT , nonlinear solutions of amplitude epsilon bifurcate. To leading order in epsilon such systems (including the case of coupled van der Pol oscillators) have behaviors governed by the single parameter rho approx. 2( delta minus gamma )/( gamma minus gamma //c). rho has a critical value rho //c determined by a Josephson-junction equation. For vertical rho vertical greater than **c rho //c the oscillations are quasiperiodic; the modulations die out in the far-from-resonance case vertical rho vertical yields infinity . For vertical rho vertical less than rho //c there are phase-locked oscillations and competing stable states can occur. An increase in lambda , causing vertical rho vertical to cross rho //c, results in a type of reverse bifurcation (quasiperiodic to periodic). No chaotic behavior is found.

Original languageEnglish (US)
Title of host publicationUnknown Host Publication Title
PublisherNorth-Holland (Mathematics Studies 80)
Pages1-5
Number of pages5
ISBN (Print)0444866779, 9780444866776
StatePublished - 1983

Publication series

Name
Volume80

ASJC Scopus subject areas

  • Engineering(all)

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