  We study the coherent and dissipative aspects of a driven spin-1
Bose-Einstein condensate (BEC) when the Zeeman energy is modulated around a
static bias value. Resonances appear when the bias energy matches an integer
number of modulation quanta. They constitute the atomic counterpart of Shapiro
resonances observed in microwave-driven superconducting Josephson junctions.
The population dynamics near each resonance corresponds to slow and non-linear
secular oscillations on top of a rapid `micromotion'. At long times and in a
narrow window of modulation frequencies around each resonance, we observe a
relaxation to asymptotic states that are unstable without drive. These
stationary states correspond to phase-locked solutions of the Josephson
equations generalized to include dissipation, and are analogous to the
stationary states of driven superconducting junctions. We find that dissipation
is essential to understand this long-time behavior, and we propose a
phenomenological model to explain quantitatively the experimental results.
Finally, we demonstrate hysteresis in the asymptotic state of the driven spinor
BEC when sweeping the modulation frequency across a Shapiro resonance.
