  Our goal is to relate the photometric and spectroscopic variability of
classical T Tauri stars, of the star-forming cluster NGC 2264, to the physical
processes acting in the stellar and circumstellar environment, within a few
stellar radii from the star. NGC 2264 was the target of a multiwavelength
observational campaign with CoRoT, MOST, Spitzer, and Chandra satellites and
observations from the ground. We classified the CoRoT light curves of accreting
systems according to their morphology and compared our classification to
several accretion diagnostics and disk parameters. The morphology of the CoRoT
light curve reflects the evolution of the accretion process and of the inner
disk region. Accretion burst stars present high mass-accretion rates and
optically thick inner disks. AA Tau-like systems, whose light curves are
dominated by circumstellar dust obscuration, show intermediate mass-accretion
rates and are located in the transition of thick to anemic disks. Classical T
Tauri stars with spot-like light curves correspond mostly to systems with a low
mass-accretion rate and low mid-IR excess. About 30% of the classical T Tauri
stars observed in the 2008 and 2011 CoRoT runs changed their light-curve
morphology. Transitions from AA Tau-like and spot-like to aperiodic light
curves and vice versa were common. The analysis of the $H\alpha$ emission line
variability of 58 accreting stars showed that 8 presented a periodicity that in
a few cases was coincident with the photometric period. The blue and red wings
of the $H\alpha$ line profiles often do not correlate with each other,
indicating that they are strongly influenced by different physical processes.
Accreting stars have a dynamic stellar and circumstellar environment that can
be explained by magnetospheric accretion and outflow models, including
variations from stable to unstable accretion regimes on timescales of a few
years
