It is shown the effect of the interfacial Dzyaloshinskii–Moriya Interaction (i-DMI) on the topology of droplets excited by a localized perpendicular spin-polarized current. According to micromagnetic simulations it is demonstrated that the phase diagram i-DMI as a function of the polarized current at zero magnetic field exhibits a complex scenario with regions characterized by static and dynamic states. In the dynamical part, it is possible to identify topological stable and unstable regions. The topological stable regions are linked to the excitation of droplets with skyrmion number either equal to one (topological) or zero (non-topological). The zero skyrmion number droplets are characterized by the non-stationary time domain excitation of both topological and non-topological droplet modes. The transition between these two modes is coupled to an emission of incoherent spin-waves. It is also developed an analytical model demonstrating that the topological droplet mode can be seen as a linear radial mode of a static skyrmion state stabilized by a perpendicular spin-polarized current. The results obtained by means of the analytical model confirm the red-shift behaviour of the topological mode frequencies as a function of the current density predicted by micromagnetic simulations. The interplay between topology and dynamics is discussed by introducing the notion of topological degeneracy and the non-reciprocal role of the spin polarized current on the topological mode dynamics is highlighted
