We investigated the application of non-linear analysis techniques for capturing stability of neural oscillatory activity within and across brains. Recurrence Quantification Analysis (RQA), a technique that has been applied to detect stability and flexibility of motor performance, was extended to observe and quantify changes in patterns of non-linear neural activity. Participants synchronized their finger-tapping with a confederate partner who tapped at two different rhythms while neural activity was recorded from both partners using electroencephalography (EEG). Auto-recurrence (intra-brain) and cross-recurrence (inter-brain) of EEG activity were able to distinguish differences across tapping rhythms in stability of neural oscillatory activity. We also demonstrated the efficacy of RQA to capture how both period and phase changes in neural dynamics evolve over time.