  We report on bifurcations effect mediated by the electron-phonon coupling in
a concentrated rare-earth-containing antiferromagnet, observed in the spectra
of coupled $4f$-electron-phonon modes under the influence of an external
magnetic field. The effect was observed in the low-temperature far-infrared
(terahertz) reflection spectra of a multiferroic easy-axis antiferromagnet
$PrFe_3(BO_3)_4$ in magnetic fields $\textbf{B}_{ext}||c$. Both paramagnetic
and magnetically ordered phases (including a spin-flop one) were studied in
magnetic fields up to 30 T. We show that the field behavior of the coupled
modes can be successfully explained and modeled on the base of the equation
derived in the frame of the theory of coupled electron-phonon modes, with the
same field-independent electron-phonon interaction constant $|W| = 14.8
cm^{-1}$.
