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.

arXiv comment3 figures

References in corpus (4)

• Full distribution of first exit times in the narrow escape problem
• First Passage Time Densities in Resonate-and-Fire Models
• First Passage Time Densities in Non-Markovian Models with Subthreshold Oscillations
• Modeling bursting in neuronal networks using facilitation-depression and afterhyperpolarization

Cited by in corpus (1)

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