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The black hole candidates exhibit fast variability of their X-ray emission ona wide range of timescales. The short, coherent variations, with frequenciesabove 1 Hz, are referred to as quasi-periodic oscillations, and are generallyexplained by resonant effects in the black hole accretion flow. The purelystochastic variability that occurs due to turbulent conditions in the plasma,is quantified by the power density spectra and appears practically in all typesof sources and their spectral states. The specific kind of quasi-periodicflares is expected, when the global structure of the accretion flow, governedby the nonlinear hydrodynamics, induces fluctuations around a fixed pointsolution. These conditions, which occur at high accretion rates, lead to thevariability in the sense of deterministic chaos. We study the nonlinearbehaviour of X-ray sources using the recurrence analysis method. We estimatequantitatively the indications for deterministic chaos, such as the Renyi'sentropy, for the observed time series, and we compare them with the surrogatedata. Using the data collected by RXTE satellite, we reveal the oscillationspattern and the observable properties of six black hole systems. We confirmthat both the well known microquasar GRS 1915+105, as well as its recentlydiscovered analogue, IGR J17091-3624, exhibit variability characteristic todeterministic chaotic system. We conclude therefore that the underlying natureof the process must be intrinsically connected in these sources with theaccretion flow instability, that leads to the limit cycle oscillations around afixed point. Furthermore, we studied four other black hole candidates with highaccretion rates. For GX 339-4, GRO J1655-40 and XTE J1550-564 we obtainedsignificant results for some observations, whereas for XTE J1650-500 no suchdata set was found.

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