  We study the effect of noise on a Josephson junction that, coupled to a
linear $RLC$ resonator, can oscillate at two frequencies. To establish the
global stability of the attractors, we estimate the position of the separatrix,
an essential information to establish the stability of the attractor for this
multidimensional system, from the analysis of the mean first passage time. We
find that the frequency locked to the resonator is most stable at low bias, and
less stable at high bias, where the resonator exhibits the largest
oscillations. The change in the birhythmic region is dramatic, for the
effective barrier changes of an order of magnitude and the corresponding
lifetime of about seven decades.
