We have modeled the highly non-linear dynamic phenomena which arise in Gunn diodes by interaction between the internally generated domain mode and an external microwave signal. As the frequency of the microwave signal is changed, a devil's staircase of frequency-locked oscillations develops, interspersed with quasiperiodic solutions. Period- doubling and other forms of mode-converting bifurcations can be seen in the interval of some of the steps. At higher microwave amplitudes, deterministic chaos arises. The transitions to delayed, quenched, and limited space charge accumulation modes are followed.