Escape of a harmonically forced classical particle from asymmetric potential well

Abstract

The paper addresses the problem of escape of harmonically forced classical particle from asymmetric potential well. Two benchmark models of the potential wells are used – truncated parabolic well with small cubic perturbation, and more common essentially nonlinear quadratic-cubic well. Transient escape dynamics in both models is analyzed in the framework of isolated resonance approximation. Despite substantial difference between both models, the observed escape scenarios are qualitatively similar. In each case, as parameters of the system are modified, the amplitude of the slow phase flow can gradually achieve the escape threshold; this simple mechanism is referred to as "maximum" scenario. The other, potentially more dangerous scenario, involves abrupt transition of the system response from relatively small amplitude to the escape. This pattern is related to passage of the slow-flow phase trajectory through dynamical saddle of the resonant manifold, and thus is referred to as "saddle" scenario. Both escape scenarios are easily observed in full-scale numeric simulations, in complete agreement with the theoretical predictions. The aforementioned resonance escape mechanisms are similar to those which were reviled in the case of symmetric potential well. Also, both mechanisms are generic enough to remain unchanged even in presence of small damping. These findings point on an unexpected universality of the resonance escape mechanisms. Description of the motion outside the well is not included in the current study.