2019/10/18 by Maor Farid, Farid, Maor, Oleg Gendelman +1
Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Quantum chaos and dynamical systems #Spectroscopy and Quantum Chemical Studies #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.1910.08545
openalex publication_date 2019/10/18 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
Escape from a potential well is an extreme example of transient behavior. We\nconsider the escape of the harmonically forced particle under viscous damping\nfrom the benchmark truncated weakly nonlinear potential well. Main attention is\npaid to most interesting case of primary 1:1 resonance. The treatment is based\non multiple-scales analysis and exploration of the slow-flow dynamics. Contrary\nto Hamiltonian case described in earlier works, in the case with damping the\nslow-flow equations are not integrable. However, if the damping is small\nenough, it is possible to analyze the perturbed slow-flow equations. The effect\nof the damping on the escape threshold is evaluated in the explicit analytic\nform. Somewhat unexpectedly, the escape mechanisms in terms of the slow flow\nare substantially different for the linear and weakly nonlinear cases.\n