Isostables for stochastic oscillators
Dynamical Systems
2021-12-15 v2
Abstract
Thomas and Lindner (2014, Phys.Rev.Lett.) defined an asymptotic phase for stochastic oscillators as the angle in the complex plane made by the eigenfunction, having a complex eigenvalue with a least negative real part, of the backward Kolmogorov (or stochastic Koopman) operator. We complete the phase-amplitude description of noisy oscillators by defining the stochastic isostable coordinate as the eigenfunction with the least negative nontrivial real eigenvalue. Our results suggest a framework for stochastic limit cycle dynamics that encompasses noise-induced oscillations.
Cite
@article{arxiv.2105.11048,
title = {Isostables for stochastic oscillators},
author = {Alberto Pérez-Cervera and Benjamin Lindner and Peter J. Thomas},
journal= {arXiv preprint arXiv:2105.11048},
year = {2021}
}