Quantitative comparison of the mean–return-time phase and the stochastic asymptotic phase for noisy oscillators

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Pérez Cervera, Alberto and Lindner, Benjamin and Thomas, Peter J. (2022) Quantitative comparison of the mean–return-time phase and the stochastic asymptotic phase for noisy oscillators. Biological Cybernetics, 116 (2). pp. 219-234. ISSN 1432-0770

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Official URL: https://doi.org/10.1007/s00422-022-00929-6




Abstract

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.


Item Type:Article
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CRUE-CSIC (Acuerdos Transformativos 2022)

Uncontrolled Keywords:Stochastic oscillator; Phase reduction; Mean–return-time sections; Isochrons; Isostables; Neuroscience
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Mathematics > Stochastic processes
Medical sciences > Medicine > Neurosciences
ID Code:72539
Deposited On:27 May 2022 15:46
Last Modified:30 May 2022 07:05

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