  We analyze the classical and quantum dynamics of the driven dissipative
Bose-Hubbard dimer. Under variation of the driving frequency, the classical
system is shown to exhibit a bifurcation to the limit cycle, where its
steady-state solution corresponds to periodic oscillation with the frequency
unrelated to the driving frequency. This bifurcation is shown to lead to a
peculiarity in the stationary single-particle density matrix of the quantum
system. The case of the Bose-Hubbard trimer, where the discussed limit cycle
bifurcates into a chaotic attractor, is briefly discussed.
