  By analyzing the time series of RXTE/PCA data, the nonlinear variabilities of
compact sources have been repeatedly established. Depending on the variation in
temporal classes, compact sources exhibit different nonlinear features.
Sometimes they show low correlation/fractal dimension, but in other classes or
intervals of time they exhibit stochastic nature. This could be because the
accretion flow around a compact object is a nonlinear general relativistic
system involving magnetohydrodynamics. However, the more conventional way of
addressing a compact source is the analysis of its spectral state. Therefore,
the question arises: What is the connection of nonlinearity to the underlying
spectral properties of the flow when the nonlinear properties are related to
the associated transport mechanisms describing the geometry of the flow? The
present work is aimed at addressing this question. Based on the connection
between observed spectral and nonlinear (time series) properties of two X-ray
binaries: GRS 1915+105 and Sco X-1, we attempt to diagnose the underlying
accretion modes of the sources in terms of known accretion classes, namely,
Keplerian disc, slim disc, advection dominated accretion flow (ADAF) and
general advective accretion flow (GAAF). We explore the possible transition of
the sources from one accretion mode to others with time. We further argue that
the accretion rate must play an important role in transition between these
modes.
