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Forced frequency locking of rotating waves

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Abstract

We describe the frequency locking of an asymptotically orbitally stable rotating wave solution of an autonomous S1-equivariant differential equation under the forcing of a rotating wave.

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References

  1. N. V. Butenin, Yu. I. Neimark, and N. A. Fufaev, Introduction to the Theory of Nonlinear Oscillations [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  2. C. Chicone, “Bifurcations of nonlinear oscillations and frequency entrainment near resonance,” SIAM J. Math. Anal, 23, 1577–1608 (1992).

    Article  MATH  MathSciNet  Google Scholar 

  3. S. N. Chow and J. K. Hale, Methods of Bifurcation Theory, Springer-Verlag, New York (1982).

    MATH  Google Scholar 

  4. J. Cronin, Differential Equations. Introduction and Qualitative Theory, Marcel Dekker, New York (1994).

    MATH  Google Scholar 

  5. J. K. Hale and Z. Táboas, “Interaction of damping and forcing in a second order equation,” Nonlinear Anal. TMA., 2, 77–84 (1978).

    Article  MATH  Google Scholar 

  6. D. Rand, “Dynamics and symmetry. Predictions of modulated waves in rotating fluids,” Arch. Rat. Mech. Anal., 75, 1–38 (1982).

    Article  MathSciNet  Google Scholar 

  7. C. Z. Ning and H. Haken, “The geometric phase in nonlinear dissipative systems,” Mod. Phys. Lett. B, 6, 1541–1568 (1992).

    Article  MathSciNet  Google Scholar 

  8. M. Renardy, “Bifurcation from rotating waves,” Arch. Rat. Mech. Anal., 79, 43–84 (1982).

    MathSciNet  Google Scholar 

  9. M. Renardy and H. Haken. “Bifurcation of solutions of the laser equations,” Phvs. D, 8, 57–89 (1983).

    Article  MathSciNet  Google Scholar 

  10. A. M. Samoilenko, Mathematical Theory of Multifrequency Oscillations, Kluwer, Dordrecht (1991).

    Google Scholar 

  11. J. K. Hale, Ordinary Differential Equations, Wiley, New York (1969).

    MATH  Google Scholar 

  12. L. Recke and D. Peterhof, “Abstract forced symmetry breaking and forced frequency locking of modulated waves,” J. Different. Equat. (1998) (to appear).

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Authors and Affiliations

  1. Institute of Mathematics, Humboldt University, Berlin, Germany

    L. Recke

Authors
  1. L. Recke
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Published in Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 1, pp. 94–101, January, 1998.

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Recke, L. Forced frequency locking of rotating waves. Ukr Math J 50, 108–115 (1998). https://doi.org/10.1007/BF02514692

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  • DOI: https://doi.org/10.1007/BF02514692

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