Stochastic resonance in second-order autonomous systems subjected only to white noise (Q2773127)

This paper studies the phenomenon of stochastic resonance (SR) of an under-damped single pendulum driven by a constant force plus noise perturbation. The corresponding stochastic differential equation in dimensionless form reads NEWLINE\[NEWLINE\ddot\theta+ \alpha\dot\theta+ \sin\theta=b+ D\xi(t) \tag{1}NEWLINE\]NEWLINE where \(b>0\), \(\alpha>0\) is the damping coefficient and \(\xi(t)\) is a Gaussian white noise satisfying NEWLINE\[NEWLINE\bigl\langle \xi(t)\bigr \rangle=0,\;\bigl \langle\xi(t) \xi(t')\bigr\rangle =\delta(t-t'). \tag{2}NEWLINE\]NEWLINE The main goal of this paper is to give a systematic investigation of SR in system (1). The author shows that when there is a stable node on the one-dimensional global attractor, a moderate amount of noise not only motivates the system to switch between the identical stable nodes, but also controls the timescale to induce some periodicity of the switching events.