  This paper considers a nonlinear coupling between a radial and a nonradial
mode of nearly the same frequency. The results may be of general interest, but
in particular have application to the "beating-modes model" of the Blazhko
effect which was recently shown to accurately reproduce the light curve of RR
Lyr. For weak coupling, the two modes do not phase-lock and they retain
separate frequencies, but the coupling nevertheless has important consequences.
Upon increasing the coupling strength from zero, an additional side-peak
emerges in the spectrum forming an asymmetric triplet centered on the
fundamental. As the coupling is further increased, the amplitude of this
side-peak increases and the three peaks are also pulled towards each other,
decreasing the Blazhko frequency. Beyond a critical coupling strength,
phase-locking occurs between the modes. With appropriate choice of coupling
strength, this "interactive beating-modes model" can match the side-peak
amplitude ratio of any star. The effects of nonlinear damping are also explored
and found to generate additional side-peaks of odd order. Consistent with this,
the odd side-peaks are found to be favored in V808 Cyg. It is also shown that
the Blazhko effect generates a fluctuating "environment" that can have a
modulatory effect on other excited modes of the star. An example is found in
V808 Cyg where the modulation is at double the Blazhko frequency. An
explanation is found for this mysterious doubling, providing additional
evidence in favor of the model.
