We develop the physical model based on the real space charge transfer mecha
nism and derive the dynamic equations of GaAs/AlGaAs heterostructures. Comp
lex bifurcations are studied in detail for the forced and unforced cases. I
t is shown that both periodic attractors and fixed points attractors can co
exist under a right de bias. The hysteresis phenomena are also investigated
in theory. For the forced GaAs/AlGaAs, numerical simulation shows that the
occurance of frequency-locking, quasiperiodicity, and chaos depends on the
frequency and amplitude of the externally applied microwave field, as expe
cted.