Resonant activation in 2D and 3D systems driven by multi-variate L\'evy noises

TL;DR

This paper demonstrates that resonant activation occurs in 2D and 3D systems influenced by multi-variate Lévy noises, with its strength depending on specific noise parameters, especially the stability index.

Contribution

It extends the understanding of resonant activation to higher-dimensional systems driven by bi- and tri-variate Lévy noises, highlighting the sensitivity to noise parameters.

Findings

Resonant activation observed in 2D and 3D systems with multi-variate Lévy noises.

The strength of resonant activation depends on the noise parameters, especially the stability index.

Decreasing the stability index $eta$ leads to the disappearance of resonant activation.

Abstract

Resonant activation is one of classical effects demonstrating constructive role of noise. In resonant activation cooperative action of barrier modulation process and noise lead to the optimal escape kinetics as measured by the mean first passage time. Resonant activation has been observed in versatilities of systems for various types of barrier modulation processes and noise types. Here, we show that resonant activation is also observed in 2D and 3D systems driven by bi-variate and tri-variate $\alpha$-stable noises. Strength of resonant activation is sensitive to the exact value of the noise parameters. In particular, the decrease in the stability index $\alpha$ results in the disappearance of the resonant activation.