Dynamics of super-harmonic escape from truncated quasilinear and strongly non-linear potential well

The problem of escape attracted a lot of attention over an extended period of time. Recently, the analytic approach towards this sort of problem had been suggested in the context of the primary 1:1 resonance. The effect of the secondary resonances is well-known from early numeric simulations, but the analytic approach capable of predicting the escape threshold and safe basins in the space of initial conditions is still missing. In this study we address a particular case of this problem, namely a particle under super-harmonic excitation in a one degree-of-freedom weakly anharmonic truncated quartic potential well. This system itself was studied before, though not so much in the context of analytic approaches.