The Gentlest Ascent Dynamics

TL;DR

This paper introduces a dynamical system framework to identify saddle points, including high index ones, in both gradient and non-gradient systems, providing insights into escape dynamics from stable attractors.

Contribution

It presents a novel dynamical system approach to locate saddle points of various indices, extending previous methods to high index saddle points and non-gradient systems.

Findings

Stable fixed points of the proposed dynamics are index-1 saddle points.

Generalizations to high index saddle points are discussed.

Preliminary results reveal the behavior of the dynamical systems near saddle points.

Abstract

Dynamical systems that describe the escape from the basins of attraction of stable invariant sets are presented and analyzed. It is shown that the stable fixed points of such dynamical systems are the index-1 saddle points. Generalizations to high index saddle points are discussed. Both gradient and non-gradient systems are considered. Preliminary results on the nature of the dynamical behavior are presented.