  We consider a damped $\beta$-Fermi-Pasta-Ulam chain, driven at one boundary
subjected to stochastic noise. It is shown that, for a fixed driving amplitude
and frequency, increasing the noise intensity, the system's energy resonantly
responds to the modulating frequency of the forcing signal. Multiple peaks
appear in the signal to noise ratio, signalling the phenomenon of stochastic
resonance. The presence of multiple peaks is explained by the existence of many
stable and metastable states that are found when solving this boundary value
problem for a semi-continuum approximation of the model. Stochastic resonance
is shown to be generated by transitions between these states.
