Pseudopotential of birhythmic van der Pol type systems with correlated noise

TL;DR

This paper develops a method to compute the effective activation energy, or pseudopotential, for a birhythmic van der Pol oscillator under correlated noise, demonstrating its validity through analytical and numerical approaches.

Contribution

It introduces a way to incorporate correlated noise into the pseudopotential framework for birhythmic systems, extending the understanding of their stability.

Findings

Correlated noise can be effectively included in pseudopotential calculations.

The pseudopotential accurately predicts escape rates in birhythmic systems.

The approach is validated through analytical and numerical methods.

Abstract

We propose to compute the effective activation energy, usually referred to a pseudopotential or quasipotential, of a birhythmic system -- a van der Pol like oscillator -- in the presence of correlated noise. It is demonstrated, with analytical techniques and numerical simulations, that the correlated noise can be taken into account and one can retrieve the low noise rate of the escapes. We thus conclude that a pseudopotential, or an effective activation energy, is a realistic description for the stability of birhythmic attractors also in the presence of correlated noise.