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Chaotic and stochastic processes in the accretion flows of the black hole X-ray binaries revealed by recurrence analysis

The black hole candidates exhibit fast variability of their X-ray emission on a wide range of timescales. The short, coherent variations, with frequencies above 1 Hz, are referred to as quasi-periodic oscillations, and are generally explained by resonant effects in the black hole accretion flow. The purely stochastic variability that occurs due to turbulent conditions in the plasma, is quantified by the power density spectra and appears practically in all types of sources and their spectral states. The specific kind of quasi-periodic flares is expected, when the global structure of the accretion flow, governed by the nonlinear hydrodynamics, induces fluctuations around a fixed point solution. These conditions, which occur at high accretion rates, lead to the variability in the sense of deterministic chaos. We study the nonlinear behaviour of X-ray sources using the recurrence analysis method. We estimate quantitatively the indications for deterministic chaos, such as the Renyi's entropy, for the observed time series, and we compare them with the surrogate data. Using the data collected by RXTE satellite, we reveal the oscillations pattern and the observable properties of six black hole systems. We confirm that both the well known microquasar GRS 1915+105, as well as its recently discovered analogue, IGR J17091-3624, exhibit variability characteristic to deterministic chaotic system. We conclude therefore that the underlying nature of the process must be intrinsically connected in these sources with the accretion flow instability, that leads to the limit cycle oscillations around a fixed point. Furthermore, we studied four other black hole candidates with high accretion rates. For GX 339-4, GRO J1655-40 and XTE J1550-564 we obtained significant results for some observations, whereas for XTE J1650-500 no such data set was found.