L\'evy noise induced transitions and enhanced stability in a birhythmic van der Pol system

TL;DR

This paper investigates how Le9vy noise influences transitions and stability in a birhythmic van der Pol oscillator, revealing that noise-induced escapes behave similarly to those in potential systems, with notable differences near a specific distribution index.

Contribution

It provides new insights into the effects of Le9vy noise on birhythmic oscillators, highlighting differences from Gaussian noise especially near a distribution index of two.

Findings

Noise-induced escapes resemble those in potential systems.

Differences are more significant when the Le9vy distribution index is close to two.

Attractors are separated by a pseudo-potential barrier.

Abstract

This work describes the effects of L\'evy noise on a birhythmic van der Pol like oscillator. Numerical simulations demonstrate that the noise induced escapes from an attractor to another are not markedly different from escapes between stable points in an ordinary potential, albeit the attractors are separated by a barrier of a quasi (or pseudo) potential. However, some differences appear, and are more pronounced when the L\'evy distribution index is close to two.