Semiconductor nano-lasers have been a topic of interest from the perspective of advancing the capabilities of photonic integration. Nano-lasers are perceived as the means to achieve improved functionality in photonic integrated circuits. The properties and performance of nano-lasers have been examined by means of simulations and laboratory measurements. Nano-lasers lend themselves to integration to form dense arrays in both one and two dimensions. In a recent work, a theoretical treatment was presented for the dynamic behaviour of stand-alone electrically pumped nano-laser arrays. In this work, the response of nano-laser arrays to direct current modulation is examined. As in previous works, attention is given to two prototype array geometries: a linear three-element linear array and an equilateral triangular array. Large one-dimensional arrays can be built by repeating this elementary linear array. Two-dimensional photonic integrated circuits can incorporate the triangular arrays studied here. Such prototypical configurations offer opportunities to tailor the modulation response of the nano-laser arrays. The principal factors which provide that capability are the coupling strengths between lasers in the arrays and the direct modulation parameters. The former are fixed at the design and manufacture stage of the array whilst the latter can be chosen. In addition, the enhancement of the spontaneous emission rate via the so-called Purcell effect in nano-lasers offers a device-specific means for accessing a range of modulation responses. Two-dimensional portraits of the regimes of differing modulation responses offer a convenient means for determining the dynamics that may be accessed by varying the laser drive current. It is shown by these means that a rich variety of modulation responses can be accessed in both linear and triangular arrays.