  The paper presents an analytical approach for predicting the safe basins (SB)
in a plane of initial conditions (IC) for escape of classical particle from the
potential well under harmonic forcing. The solution is based on the
approximation of isolated resonance, which reduces the dynamics to conservative
flow on a two-dimensional resonance manifold (RM). Such a reduction allows easy
distinction between escaping and non-escaping ICs. As a benchmark potential, we
choose a common parabolic-quartic well with truncation at varying energy
levels. The method allows accurate predictions of the SB boundaries for
relatively low forcing amplitudes. The derived SBs demonstrate an unexpected
set of properties, including decomposition into two disjoint zones in the IC
plane for a certain range of parameters. The latter peculiarity stems from two
qualitatively different escape mechanisms on the RM. For higher forcing values,
the accuracy of the analytic predictions decreases to some extent due to the
inaccuracies of the basic isolated resonance approximation, but mainly due to
the erosion of the SB boundaries caused by the secondary resonances.
Nevertheless, even in this case the analytic approximation can serve as a
viable initial guess for subsequent numeric estimation of the SB boundaries.
