Nonlinear time series analysis of the light curves from the black hole system GRS1915＋105

GRS 1915+105 is a prominent black hole system exhibiting variability over a wide range of time scales and its observed light curves have been classified into 12 temporal states. Here we undertake a complete analysis of these light curves from all the states using various quantifiers from nonlinear time series analysis, such as the correlation dimension (D2), the correlation entropy (K2), singular value decomposition (SVD) and the multifractal spectrum (f(α) spectrum). An important aspect of our analysis is that, for estimating these quantifiers, we use algorithmic schemes which we have recently proposed and successfully tested on synthetic as well as practical time series from various fields. Though the schemes are based on the conventional delay embedding technique, they are automated so that the above quantitative measures can be computed using conditions prescribed by the algorithm and without any intermediate subjective analysis. We show that nearly half of the 12 temporal states exhibit deviation from randomness and their complex temporal behavior could be approximated by a few (three or four) coupled ordinary nonlinear differential equations. These results could be important for a better understanding of the processes that generate the light curves and hence for modeling the temporal behavior of such complex systems. To our knowledge, this is the first complete analysis of an astrophysical object (let alone a black hole system) using various techniques from nonlinear dynamics.