Escape of a forced-damped particle from weakly nonlinear truncated potential well

Abstract

Abstract Escape from a potential well is an extreme example of transient behavior. We consider the escape of the harmonically forced particle under viscous damping from the benchmark truncated weakly nonlinear potential well. Main attention is paid to most interesting case of primary 1:1 resonance. The treatment is based on multiple-scales analysis and exploration of the slow-flow dynamics. Contrary to Hamiltonian case described in earlier works, in the case with damping the slow-flow equations is not integrable. However, if the damping is small enough, it is possible to analyze the perturbed slow-flow equations. The effect of the damping on the escape threshold is evaluated in an explicit analytic form. The substantial difference between the linear and weakly nonlinear cases in terms of the slow-flow dynamics of the escape mechanisms is demonstrated and discussed.