  We analyze global stability properties of birhythmicity in a self-sustained
system with random excitations. The model is a multi-limit cycles variation of
the van der Pol oscillatorintroduced to analyze enzymatic substrate reactions
in brain waves. We show that the two frequencies are strongly influenced by the
nonlinear coefficients $\alpha$ and $\beta$. With a random excitation, such as
a Gaussian white noise, the attractor's global stability is measured by the
mean escape time $\tau$ from one limit-cycle. An effective activation energy
barrier is obtained by the slope of the linear part of the variation of the
escape time $\tau$ versus the inverse noise-intensity 1/D. We find that the
trapping barriers of the two frequencies can be very different, thus leaving
the system on the same attractor for an overwhelming time. However, we also
find that the system is nearly symmetric in a narrow range of the parameters.
