This study proposes a time-series analysis approach and a non-linear dynamics originated method to detect sub-synchronous oscillation in power systems. Mathematical expressions of the fundamental instantaneous signal and sample discrete signal of peak values are derived to examine the phenomenon of interaction between power system components. The results of the circulating trajectory are shown in a two-dimensional map of the calculated root-mean-square value and estimated Floquet multiplier when two signals of different modes are mixed. Without applying a digital filter or frequency decomposition, non-linear oscillation detection is possible by monitoring a non-linear oscillatory index based on the maximum Lyapunov exponent.