We studied the catalytic NO2(g) + H2(g)/Pt system on model platinum catalysts with nanoscale spatial resolution by means of field emission microscopy (FEM). While the surface of the catalyst is in a non-reactive state at low H2 partial pressure, bursts of activity are observed when increasing this parameter. These kinetic instabilities subsequently evolve towards self-sustained periodic oscillations for a wide range of pressures. Combining time series analyses and numerical simulations of a simple reaction model, we clarify how these observations fit in the traditional classification of dynamical systems. In particular, reconstructions of the probability density around oscillating trajectories show that the experimental system defines a crater-like structure in probability space. The experimental observations thus correspond to a noise-perturbed limit cycle emerging from a nanometric reactive system. This conclusion is further supported by comparison with stochastic simulations of the proposed chemical model. The obtained results and simulations pave the way towards a better understanding of reactive nanosystems.