We consider a triple zero point of nonlinear equations with O(2)-symmetry, where the Jacobian has a zero eigenvalue of geometric multiplicity one and algebraic multiplicity three, We show that this triple zero point exhibits a new bifurcation phenomenon, that is, a mode interaction of the following three paths: bifurcation points from steady-states, steadystates and rotating waves to standing waves, rotating waves and modulated rotating waves respectively.
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