A theoretical analysis is performed on the response of electrically pumped nano-laser arrays to external optical injection. The response to both continuous wave and modulated optical injection is explored. Continuous wave injection is shown to excite several varieties of dynamical behaviour in the array elements including regular dynamics and quasi-periodic behaviour. The strength of the optical injection, the frequency detuning between the injected light and the target laser, and the magnitude of the Purcell spontaneous emission enhancement factor are shown to markedly affect the dynamics. When subject to modulated optical injection, the effects of frequency detuning and optical injection strength are the focus of attention. It is shown that the elements of the array subject to modulated optical injection exhibit oscillatory behaviour over broad regimes determined by the optical injection strength and the frequency detuning.