Metastable switching in a planar limit cycle system with additive noise

• Noisy limit cycle systems can behave like Brownian motion in a periodic potential.
• Metastable switching is caused by nonlinear interactions between dynamics and noise.
• One example displays rare switching even with strong additive noise.
• Metastability is analyzed with asymptotic phase reduction and numerical simulations.
• Rare switching occurs when the nonlinear dynamics filter and weaken the phase noise.

Additive noise is known to produce counter-intuitive behaviors in nonlinear dynamical systems. Previously, it was shown that systems with a deterministic limit cycle can display switching between metastable states in the presence of asymmetric additive white noise. Here, we systematically analyze the dynamics of this metastable behavior and show how the vector field away from the limit cycle influences the rate and directionality of the metastable switching. Using stochastic phase reduction methods as well as asymptotic approximations, we identify mechanisms underlying different rates of switching and predict when the system will rotate in the opposite direction of the deterministic limit cycle. Thus, this work presents an alternative mechanism for generating a range of metastable switch behaviors that have been observed in a number of physical systems.