Escape from an attractor generated by recurrent exit

TL;DR

This paper investigates how stochastic trajectories can repeatedly re-enter a basin of attraction due to shallow potentials, affecting escape times and explaining neuronal burst durations.

Contribution

It introduces a new understanding of escape dynamics in shallow potential systems, highlighting multiple re-entries before escape.

Findings

High probability of return inside the basin before escape

Distribution of escape times computed and analyzed

Explains variability in neuronal interburst durations

Abstract

Kramer's theory of activation over a potential barrier consists in computing the mean exit time from the boundary of a basin of attraction of a randomly perturbed dynamical system. Here we report that for some systems, crossing the boundary is not enough, because stochastic trajectories return inside the basin with a high probability a certain number of times before escaping far away. This situation is due to a shallow potential. We compute the mean and distribution of escape times and show how this result explains the large distribution of interburst durations in neuronal networks.