Stochastic basins of attraction and generalized committor functions

TL;DR

This paper extends the concept of basins of attraction to noisy dynamical systems using Markov chains, enabling analysis of metastability and long transients through generalized committor functions.

Contribution

It introduces a generalized framework for basins of attraction in stochastic systems, linking mean sojourn times and absorption probabilities to stability analysis.

Findings

Applicable to diverse dynamical systems via transfer operator approximation

Provides a method to analyze metastable states and long transients

Connects Markov chain properties with basin stability

Abstract

We generalize the concept of basin of attraction of a stable state in order to facilitate the analysis of dynamical systems with noise and to assess stability properties of metastable states and long transients. To this end we examine the notions of mean sojourn times and absorption probabilities for Markov chains and study their relation to the basins of attraction. Our approach is applicable to a large variety of problems since in most cases the transfer operator associated to a dynamical system can be approximated by a Markov chain.