In this study, the coefficient of friction (COF) signals throughout the running-in process were examined by sliding a ring against a static disc. By reconstructing the scalar time-series into multi-dimensional phase spaces, friction-induced attractors were obtained and quantified by recursive characteristics analysis, which can effectively realize the running-in status identification. Moreover, a recursive characteristics analysis-based evaluation model was established to investigate the stationarity of the friction-induced attractors based on the recurrence quantification analysis (RQA) measures. The analyses of the numerically simulated signals and experimental results indicate that the extracted model is an intuitive and effective method. Furthermore, to improve the stationary of the friction-induced attractors, the normal pressure should be low, whereas the relative sliding velocities should be increased appropriately. These results would contribute to the revelation of the recursive characteristics of the tribosystem and the improvement of the stationarity of friction-induced attractors.