Scaling in activated escape of underdamped systems

TL;DR

This paper investigates how the activation energy for noise-induced escape in underdamped dynamical systems scales near a saddle-node bifurcation, revealing two types of scaling laws and critical exponents.

Contribution

It identifies two distinct scaling regimes and their critical exponents for escape activation energy in underdamped systems near bifurcation points.

Findings

Two types of scaling laws for activation energy are identified.

Critical exponents for each scaling law are determined.

Results enhance understanding of noise-induced escape in underdamped systems.

Abstract

Noise-induced escape from a metastable state of a dynamical system is studied close to a saddle-node bifurcation point, but in the region where the system remains underdamped. The activation energy of escape scales as a power of the distance to the bifurcation point. We find two types of scaling and the corresponding critical exponents.