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Original Articles

Resonance Surfaces for Forced Oscillators

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Pages 221-244 | Published online: 03 Apr 2012

REFERENCES

  • Arnol'd , V. I. 1982 . Geometric Methods in the Theory of Ordinary Differential Equations New York : Springer. . [Arnol'd 1982]
  • Aronson , D. , Chory , M. , Hall , G. and McGehee , R. 1982 . “Bifurcations from an invariant circle for two-parameter families of maps of the plane: a computer-assisted study” . Comm. Math. Phys. , 83 : 304 – 354 . [Aronson et al. 1982]
  • Aronson , D. , McGehee , R. , Kevrekidis , I. and Aris , R. 1986 . “Entrainment regions for periodically forced oscillators” . Phys. Rev. , A33 : 2190 – 2192 . [Aronson et al. 1986]
  • Bogdanov , R. I. 1976 . “A versal deformation of a singular point of a vector field in the plane in the case of vanishing eigenvalues”. ” . In Trudy Seminara Imeni I. G. Petrovskogo Vol. 2 , 37 – 65 . [Bogdanov 1976], (in Russian), English translation, Selecta Math. Sovietica 1 (1981), 373–388
  • Chenciner , A. 1985 . “Bifurcation de points fixes elliptiques. II. Orbites periodiques et ensembles de Cantor invariants” . Inv. Math. , 80 : 81 – 106 . [Chenciner 1985]
  • Frouzakis , C. E. , Adomaitis , R. A. and Kevrekidis , I. G. 1991 . “Resonance phenomena in an adaptivelly-controlled system” . Int. J. Bifurcations and Chaos , 1 : 83 – 106 . [Frouzakis et al. 1991]
  • Guckenheimer , J. and Holmes , P. 1983 . Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields New York : Springer. . [Guckenheimer and Holmes 1983]
  • Hall , G. R. 1984 . “Resonance Zones in two-parameter families of circle homeomorphisms” . SIAM J. Math. Anal. , 15 : 1075 – 1081 . [Hall 1984]
  • Kai , T. and Tomita , K. 1979 . “Stroboscopic phase portrait of a forced nonlinear oscillator” . Progr. Theor. Phys. , 61 : 54 – 73 . [Kai and Tomita 1979]
  • Kevrekidis , I. G. , Aris , R. and Schmidt , L. D. 1986 . “The stirred tank forced” . Chem. Eng. Sci. , 41 : 1549 – 1560 . [Kevrekidis et al. 1986]
  • McGehee , R. P. and Peckham , B. B. 1992 . “Resonance City” The Geometry Center, University of Minnesota. . [McGehee and Peckham 1992], (10-minute video)
  • McGehee , R. P. and Peckham , B. B. “Determining the Global Topology of Resonance Surfaces for Periodically Forced Oscillator Families” . Proceedings of the Workshop on Normal Forms and Homoclinic Chaos . Providence , RI : Fields Institute Communications Series, Amer. Math. Soc. . [McGehee and Peckham 1995]
  • Peckham , B. 1988 . “The closing of resonance horns for periodically forced oscillators” , Ph.D. Thesis University of Minnnesota. . [Peckham 1988]
  • Peckham , B. 1990 . “The necessity of the Hopf bifurcation for periodically forced oscillators” . Nonlinearity , 3 : 261 – 280 . [Peckham 1990]
  • Peckham , B. and Kevrekidis , I. 1991 . “Period doubling with higher order degeneracies” . SIAM J. Math. Anal. , 22 : 1552 – 1574 . [Peckham and Kevrekidis 1991]
  • Phillips , M. , Levy , S. and Munzner , T. 1993 . “Geomview: An Interactive Geometry Viewer” . Notices of the Amer. Math. Soc. , 40 : 985 – 988 . [Phillips et al. 1993], This software and the accompanying manual are avialable by anonymous ftp from the host geom. umn. edu, in directory pub/software
  • Schreiber , I. , Dolnik , M. , Choc , P. and Marek , M. 1988 . “Resonance behaviour in two-parameter families of periodically forced oscillators” . Phys. Let. , A128 : 66 – 70 . [Schrieber et al. 1988]
  • Takens , F. 1974 . “Forced oscillations and bifurcations” . Coram. Math. Inst. Rijksuniversiteit Utrecht , 3 : 1 – 59 . [Takens 1974]
  • Vance , W. and Ross , J. 1989 . “A detailed study of a forced chemical oscillator: Arnold tongues and bifurcation sets” . J. Chem. Phys. , 91 : 7654 – 7670 . [Vance and Ross 1989]

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