Random perturbations of nonlinear oscillators: Homogenization and large deviations

This paper considers two prototypical strongly nonlinear oscillators with weak dissipation and noise: a pendulum which is acted on by a small noisy torque and opposed by a friction; and the noisy Duffing-van der Pol oscillator. But over a long time the weak dissipative and noise effects can be significant. This paper develops asymptotic techniques based on averaging and large deviations to study the effects of weak noise on the escape from the domain of attraction of stable equilibrium points and limit cycles in phase-space.