Double Hopf Bifurcation with Huygens Symmetry

  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},
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
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