  The second and the third order anisotropic flow, $V_{2}$ and $V_3$, are
mostly determined by the corresponding initial spatial anisotropy coefficients,
$\varepsilon_{2}$ and $\varepsilon_{3}$, in the initial density distribution.
In addition to their dependence on the same order initial anisotropy
coefficient, higher order anisotropic flow, $V_n$ ($n > 3$), can also have a
significant contribution from lower order initial anisotropy coefficients,
which leads to mode-coupling effects. In this Letter we investigate the linear
and non-linear modes in higher order anisotropic flow $V_n$ for $n=4$, $5$, $6$
with the ALICE detector at the Large Hadron Collider. The measurements are done
for particles in the pseudorapidity range $|\eta| < 0.8$ and the transverse
momentum range $0.2 < p_{\rm T} < 5.0$ GeV/$c$ as a function of collision
centrality. The results are compared with theoretical calculations and provide
important constraints on the initial conditions, including initial spatial
geometry and its fluctuations, as well as the ratio of the shear viscosity to
entropy density of the produced system.
