RT Journal Article
T1 Quantitative comparison of the mean–return-time phase and the stochastic asymptotic phase for noisy oscillators
A1 Pérez Cervera, Alberto
A1 Lindner, Benjamin
A1 Thomas, Peter J.
AB Seminal work by A. Winfree and J. Guckenheimer showed that a deterministic phase variable can be defined either in terms of Poincaré sections or in terms of the asymptotic (long-time) behaviour of trajectories approaching a stable limit cycle. However, this equivalence between the deterministic notions of phase is broken in the presence of noise. Different notions of phase reduction for a stochastic oscillator can be defined either in terms of mean–return-time sections or as the argument of the slowest decaying complex eigenfunction of the Kolmogorov backwards operator. Although both notions of phase enjoy a solid theoretical foundation, their relationship remains unexplored. Here, we quantitatively compare both notions of stochastic phase. We derive an expression relating both notions of phase and use it to discuss differences (and similarities) between both definitions of stochastic phase for (i) a spiral sink motivated by stochastic models for electroencephalograms,(ii) noisy limit-cycle systems-neuroscience models, and (iii) a stochastic heteroclinic oscillator inspired by a simple motor-control system.
PB Springer Nature
SN 1432-0770
YR 2022
FD 2022-03-23
LK https://hdl.handle.net/20.500.14352/71540
UL https://hdl.handle.net/20.500.14352/71540
LA eng
NO CRUE-CSIC (Acuerdos Transformativos 2022)
NO National Science Foundation (NSF)
NO National Institute of Health (NIH)
DS Docta Complutense
RD 13 abr 2025