Stochastic dynamics of a nonlinear oscillator driven by periodic force with slowly varying frequency

Abstract

The topology of phase portraits for nonlinear oscillators driven by a periodic force undergoes significant changes within a narrow interval of the driving force frequencies v. This property leads to nonintegrability of the equations of motion, and stochastization of their solutions when v is periodically modulated. Such behavior is due to the violation of adiabaticity and destruction of the integral manifolds, accompanied by topological rearrangements of the integral curves. We study specific features of such stochastic dynamics in a wide range of modulation periods and damping decrements.