Abstract
We consider the Hopf points emanating from Takens-Bogdanov points of non-linear systems with Z2-symmetry. Conditions for the nondegeneracy of the Hopt points are deduced. While a Hopf point predicts the possibility of a bifurcation from the steady-state solutions to periodic orbits, the nondegeneracy guarantees the certainty of the bifurcation.
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