For the polarization switching (PS) and the nonlinear dynamic behaviors (NDBs) of the optically injected laser system composed of master vertical-cavity surface-emitting laser (M-VCSEL) and slave vertical-cavity surface-emitting laser (S-VCSEL), we put forward a novel manipulation scheme and explore their control law by means of electro-optic (EO) modulation with quasi-phase matched technology in periodically poled LiNbO3. It is found that the PS of the S-VCSEL subjected to parallel or orthogonal optical injection undergoes a change of periodic oscillation with the applied transverse electric field. The envelope trajectory of the oscillation peak appears to be a cosine curve, and that of the oscillation wave trough becomes a sine curve. Besides, the PS of the S-VCSEL only depends on the applied transverse electric field and the bias current of the M-VCSEL, and is independent of the bias current of the S-VCSEL. When the bias current of the M-VCSEL takes a different value, the PS of the S-VCSEL shows a different evolution law in one period of the applied electric field. For a certain fixed bias current of the M-VCSEL, the optically injected S-VCSEL can emit an arbitrary polarization mode and its NDBs experience different evolutions when the light from the M-VCSEL goes through EO intensity modulation. If the output light of the M-VCSEL is subjected to EO intensity modulation and EO phase modulation simultaneously, while the bias current of the S-VCSEL is fixed at 1.06, that of the M-VCSEL is fixed at 1.18, and the optical injection strength is set at 5 ns-1, then the output polarization of the S-VCSEL is in turn switched from the y-LP to the left-handed elliptic polarization (EP), then the right-handed EP circular polarization, and lastly the left-handed EP. And its NDB shows in turn a single period, four doubled periods, chaos, four doubled periods, and chaos with the increase of the applied electric field.