Numerical simulation is applied to study the highly nonlinear-dynamic phenomena that can arise in Gunn diodes by interaction between the internally generated domain mode and an external microwave signal. By adjusting the time of domain formation and the speed of propagation, the internal oscillation entrains with the external signal. This produces a devil's staircase of frequency-locked solutions. At higher microwave amplitudes, period doubling and other forms of mode-converting bifurcations can be seen. In this interval the diode also exhibits spatiotemporal chaos. At still higher microwave amplitudes, transitions to delayed, quenched, and limited space-charge accumulation modes take place.