Role of nonlinear dissipation in the suppression of chaotic escape from a potential well

The inhibition of chaotic escape from a universal escape oscillator due to a periodic parametric perturbation of the quadratic potential term is studied theoretically by means of Poincare-Melnikov-Arnold analysis, and the predictions are tested against numerical simulations based on a high-resolution grid of initial conditions. It is shown that chaotic escape suppression is impossible under period-1 and period-2 parametric perturbations. The role of a nonlinear damping: term, proportional to the nth power of the velocity, on the inhibition scenario is also discussed. (C) 2001 Elsevier Science B.V. All rights reserved.