Nonlinear dynamics of continuous-wave pumped regenerative amplifiers operating at 2 μm are investigated. At repetition rates near 1 kHz, three different operation regimes are observed, including stable regular, chaotic, and subharmonic dynamics. Numerical simulations reproduce this behavior in a quantitative way. In particular, we find stable periodic doubling regimes in which every other seed pulse experiences high gain. Exploiting a narrow parameter window beyond the onset of chaos enables operation of a high-gain picosecond Ho:YLF regenerative amplifier which delivers up to 16 mJ picosecond pulses at 2050 nm. Energy fluctuations of the 700 Hz pulse train are as low as 0.9% rms.