Double Hopf Bifurcation with Huygens Symmetry

@article{Kitanov2013DoubleHB,
  title={Double Hopf Bifurcation with Huygens Symmetry},
  author={Petko M. Kitanov and William F. Langford and Allan R. Willms},
  journal={SIAM J. Applied Dynamical Systems},
  year={2013},
  volume={12},
  pages={126-174}
}
Double Hopf bifurcations have been studied prior to this work in the generic nonresonant case and in certain strongly resonant cases, including 1:1 resonance. In this paper, the case of symmetrically coupled identical oscillators, motivated by the classic problem of synchronization of Huygens’ clocks, is studied using the codimension-three Elphick–Huygens equivariant normal form presented here. The focus is on the effect that the Huygens symmetry assumption has on the dynamic behavior of the… CONTINUE READING
2 Citations
37 References
Similar Papers

Citations

Publications citing this paper.

References

Publications referenced by this paper.
Showing 1-10 of 37 references

The Operator of Translation along the Trajectories of Differential Equations

  • M. A. Krasnoselskii
  • Amer. Math. Soc. Transl. Math. Monogr., AMS…
  • 1968
Highly Influential
7 Excerpts

Normal Form Analysis for Bifurcations with Huygens Symmetry

  • P. M. Kitanov
  • Ph.D. thesis, University of Guelph, Guelph, ON…
  • 2011
Highly Influential
10 Excerpts

Elements of Applied Bifurcation Theory

  • Y. Kuznetsov
  • Springer-Verlag, New York, Berlin
  • 2004
Highly Influential
10 Excerpts

Synchronization of two coupled escapement-driven pendulum clocks

  • M. Senator
  • J. Sound and Vibration, 291
  • 2006
Highly Influential
5 Excerpts

The Mechanics of Nonlinear Systems with Internal Resonances

  • A. I. Manevich, L. I. Manevitch
  • Imperial College Press, London
  • 2005
Highly Influential
5 Excerpts

The Symmetry Perspective

  • M. Golubitsky, I. Stewart
  • Birkhäuser-Verlag, Basel, Switzerland
  • 2002
Highly Influential
5 Excerpts

Synchronization: A Universal Concept in Nonlinear Science

  • A. Pikovsky, M. Rosenblum, J. Kurths
  • Cambridge Nonlinear Sci. Ser. 12, Cambridge…
  • 2001
Highly Influential
5 Excerpts

Similar Papers

Loading similar papers…