We show that the effect of the offset phase on the dynamics of the time-delay optoelectronic oscillators that is observed experimentally can be explained in terms of switching between the subcritical and supercritical Hopf bifurcations. The domains of the offset phase for which the system functions are determined analytically. We also show that the width of these domains exceptionally depends on the interplay between the three time scales of the system. Our theoretical results fit with the experimental measurements.
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