2026-06-29T08:01:08Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/715402023-08-26T11:44:45Zcom_20.500.14352_14col_20.500.14352_15

Quantitative comparison of the mean–return-time phase and the stochastic asymptotic phase for noisy oscillators Pérez Cervera, Alberto Lindner, Benjamin Thomas, Peter J. 519.216 Stochastic oscillator Phase reduction Mean–return-time sections Isochrons Isostables Neuroscience Física-Modelos matemáticos Procesos estocásticos Neurociencias (Medicina) 1208.08 Procesos Estocásticos 2490 Neurociencias CRUE-CSIC (Acuerdos Transformativos 2022) 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. National Science Foundation (NSF) National Institute of Health (NIH) Fac. de Ciencias Matemáticas Instituto de Matemática Interdisciplinar (IMI) TRUE pub 2023-06-22T10:44:05Z 2023-06-22T10:44:05Z 2022-03-23 journal article https://hdl.handle.net/20.500.14352/71540 1432-0770 10.1007/s00422-022-00929-6 eng DMS-2052109 R01-NS118606 Atribución 3.0 España https://creativecommons.org/licenses/by/3.0/es/ open access application/pdf Springer Nature