Noise-induced transitions in a double-well excitable oscillator

Abstract: The model of a double-well oscillator with nonlinear dissipation is studied. The self-sustained oscillations regime and the excitable one are described. The first regime consists in the coexistence of two stable limit cycles in the phase space, which correspond to the self-sustained oscillations of the point mass in either potential well. The self-sustained oscillations do not occur in a noise-free system in the excitable regime, but appropriate conditions for coherence resonance in either potential well can be achieved. The stochastic dynamics in both two regimes is researched by using numerical simulation and electronic circuit implementation of the considered system. Multiple qualitative changes of the probability density function (PDF) caused by noise intensity varying are explained by using the phase space structure of the deterministic system.