  In the framework of the A Multi-Phase Transport (AMPT) model, the
multi-particle azimuthal cumulant method is used to calculate the linear and
mode-coupled contributions to the quadrangular flow harmonic ($v_{4}$),
mode-coupled response coefficient as a function of centrality in Au+Au
collisions at $\sqrt{s_{\mathrm{NN}}}$ = 200, 39, 27 and 19.6 GeV. This study
indicated that the linear and mode-coupled contributions to the $v_{4}$ are
sensitive to the beam energy change. Nevertheless, the correlations between
different order flow symmetry planes and the mode-coupled response coefficients
show a weak beam energy dependence. In addition, the presented results suggest
that the experimental measurements that span a broad range of beam energies can
be an additional constraint for the theoretical models' calculations.
