  The recently discovered phenomenon of nonlinear supratransmission consists in
a sudden increase of the amplitude of a transmitted wave triggered by the
excitation of nonlinear localized modes of the medium. We examine this process
for the Fermi-Pasta-Ulam chain, sinusoidally driven at one edge and damped at
the other. The supratransmission regime occurs for driving frequencies above
the upper band-edge and originates from direct moving discrete breather
creation. We derive approximate analytical estimates of the supratransmission
threshold, which are in excellent agreement with numerics. When analysing the
long-time behavior, we discover that, below the supratransmission threshold, a
conducting stationary state coexists with the insulating one. We explain the
bistable nature of the energy flux in terms of the excitation of quasi-harmonic
extended waves. This leads to the analytical calculation of a
lower-transmission threshold which is also in reasonable agreement with
numerical experiments.
