We develop the physical model based on the real space charge transfer mechanism and derive the dynamic equations of GaAs/AlGaAs heterostructures. Complex bifurcations are studied in detail for the forced and unforced cases. It is shown that both periodic attractors and fixed points attractors can coexist under a right dc 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 expected.