Escape from an attractor generated by recurrent exit

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.

3 figures

References in corpus (1)

• Full distribution of first exit times in the narrow escape problem

Cited by in corpus (1)

• Mesoscopic description of hippocampal replay and metastability in spiking neural networks with short-term plasticity