We present a detailed X-ray timing analysis of the highly variable NLS1 galaxy, IRAS 13224-3809. The source was recently monitored for 1.5 Ms with XMM-Newton which, combined with 500 ks archival data, makes this the best studied NLS1 galaxy in X-rays to date. We apply standard time- and Fourier-domain in order to understand the underlying variability process. The source flux is not distributed lognormally, as would be expected for accreting sources. The first non-linear rms-flux relation for any accreting source in any waveband is found, with $mathrm{rms} propto mathrm{flux}^{2/3}$. The light curves exhibit significant strong non-stationarity, in addition to that caused by the rms-flux relation, and are fractionally more variable at lower source flux. The power spectrum is estimated down to $sim 10^{-7}$ Hz and consists of multiple peaked components: a low-frequency break at $sim 10^{-5}$ Hz, with slope $alpha < 1$ down to low frequencies; an additional component breaking at $sim 10^{-3}$ Hz. Using the high-frequency break we estimate the black hole mass $M_mathrm{BH} = [0.5-2] times 10^{6} M_{odot}$, and mass accretion rate in Eddington units, $dot m_{rm Edd} gtrsim 1$. The non-stationarity is manifest in the PSD with the normalisation of the peaked components increasing with decreasing source flux, as well as the low-frequency peak moving to higher frequencies. We also detect a narrow coherent feature in the soft band PSD at $0.7$ mHz, modelled with a Lorentzian the feature has $Q sim 8$ and an $mathrm{rms} sim 3$ %. We discuss the implication of these results for accretion of matter onto black holes.
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