  We present results of variability study of a sample of 20 powerful blazars
using Fermi/LAT (0.1--300 GeV) observations. We studied decade-long
observations applying various analysis tools such as flux distribution,
symmetry analysis, and RMS-flux relation. It was found that the $\gamma$-ray
flux distribution closely resembles a log-normal probability distribution
function and can be characterized by linear RMS-flux relation. The power
spectral density analysis shows the statistical variability properties of the
sources as studied are consistent with flicker noise, an indication of
long-memory processes at work. Statistical analysis of the distribution of flux
rise and decay rates in the light curves of the sources, aimed at
distinguishing between particle acceleration and energy-dissipation timescales,
counter-intuitively suggests that both kinds of rates follow a similar
distribution and the derived mean variability timescales are on the order of a
few weeks. The corresponding emission region size is used to constrain the
location of $\gamma$-ray production sites in the sources to be a few parsecs.
Additionally, using Lomb-Scargle periodogram and weighted wavelet z-transform
methods and extensive Monte Carlo simulations, we detected year-timescale
quasi-periodic oscillations in the sources S5 0716+714, Mrk 421, ON +325, PKS
1424-418, and PKS 2155-304. We also performed recurrence quantification
analysis of the sources and directly measure the deterministic quantities,
which suggest that the dynamical processes in blazars could be a combination of
deterministic and stochastic processes, while some of the source light curves
revealed significant deterministic content.
