Parametric study and nonlinear dynamical analysis of the discharge parameter variations are presented here for a hollow cathode source in the glow discharge regime and later in the radio frequency (RF) discharge regime. A plasma source consisting of a semi‐transparent hollow cathode leads to the generation of nonthermal energetic charged particles and the formation of multiple potential regimes in the plasma column during both the glow discharge as well as the RF discharge regimes. The hollow cathode discharge obtained using this single plasma source exhibits significant mixed‐mode oscillations (MMOs) during the glow discharge regime. Various regular and irregular sequences of MMOs evolved during the progressive change of discharge voltage in the glow discharge regime. During the RF power application across the hollow cathode source, the charged particles oscillate and appear in bursts in the time series. The present study investigates energy distribution among the coherent modes of discharge through the application of the Empirical Mode Decomposition technique. Multiple coherent modes are identified during both discharge regimes that carry most of the discharge energy.