Stochastic instability of a nonlinear oscillator

The equation describing perturbed motion of a nonlinear oscillator is studied by a Hamiltonian formalism and by computer mapping. Other physical situations, including the motion of a charged particle in the field of two plane waves, the destruction of magnetic surfaces in a tokamak, and the bounce motion of a charged particle trapped in a magnetic field, can be described by the same equation. Theory predicts the regions of stochastic instability of orbits in a good agreement with computer calculations.