This paper studies dynamics of a modulation-doped GaAs/AlGaAs heterostructure under transverse magnetic fields and microwave radiations. It finds that negative differential conductivity, due to the real-space electron transfer and delayed dielectric relaxation of the interface potential barrier, can lead to complex behaviours when a relatively small magnetic field is applied. Quasiperiodicity, frequency-locking and the routes from period-doubling to chaos are found. Under a large magnetic field, however, two time-independent homogeneous steady states exist; and the longitudinal resistance of the system shows an interesting oscillation with period tuned by the ratio of microwave radiation frequency ω to the cyclotron frequency we and local minima at ω/ωc= integer + 1/4.