  As a model of coupled nano-electromechanical resonantors we study two
nonlinear driven oscillators with an arbitrary coupling strength between them.
Analytical expressions are derived for the oscillation amplitudes as a function
of the driving frequency and for the energy transfer rate between the two
oscillators. The nonlinear restoring forces induce the expected nonlinear
resonance structures in the amplitude-frequency characteristics with asymmetric
resonance peaks. The corresponding multistable behavior is shown to be an
efficient tool to control the energy transfer arising from the sensitive
response to small changes in the driving frequency. Our results imply that the
nonlinear response can be exploited to design precise sensors for mass or force
detection experiments based on nano-electromechanical resonators.
