Evolution of Non-Stationary Quasi-Periodic Pulsations in Solar Flares with Aditya-L1/HEL1OS and GOES

In the present work, we use a phase-resolved methodology for the detection and characterisation of non-stationary QPPs in the hard X-ray lightcurves observed from the HEL1OS instrument onboard Aditya-L1 mission, complemented by cross-examination using soft X-ray observations from GOES. Our approach combines variational mode decomposition with Hilbert-Huang analysis and wavelet transforms to sharpen transient QPP signatures, extract narrowband amplitude-frequency modulated modes, and track instantaneous period drift across various phases of the flares. By applying these tools to preflare, impulsive, and decay phases and associated intervals, we identify the timing, duration, and evolution of statistically significant oscillations and assess their relation to thermal and non-thermal flare components. Finally, we extend the method to the catalogue of non-stationary QPP flares reported by Mehta et al. (2023), where we identify statistically significant QPPs in both impulsive and decay phases for 74 out of 98 flares. Among these, 56.8% exhibit small period drifts, while 43.2% show larger deviations. Positive period drift dominates (73%), indicating a systematic increase in characteristic timescales as flares evolve. A phase-period-duration analysis reveals distinct regimes of non-stationarity, including overlapping multi-mode oscillations, intermittent same-period episodes, and strongly evolving multi-modal behaviour.