Estimating Phase from Observed Trajectories Using the Temporal 1-Form

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2203.04498.pdf (4.66 MB)

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https://arxiv.org/abs/2203.04498

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https://doi.org/10.48550/arXiv.2203.04498
 http://hdl.handle.net/11603/30370

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UMBC Mathematics and Statistics Department

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https://orcid.org/0000-0002-2662-6760

Date

2022-03-09

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journal articles
preprints
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Abstract

Oscillators are ubiquitous in nature, and usually associated with the existence of an “asymptotic phase” that governs the long-term dynamics of the oscillator. We show that asymptotic phase can be estimated using a carefully chosen series expansion which directly computes the phase response curve and provide an algorithm for estimating the co-efficients of this series. Unlike all previously available data driven phase estimation methods, our algorithm can: (i) use observations that are much shorter than a cycle; (ii) recover phase within any forward invariant region for which sufficient data are available; (iii) recover the phase response curves (PRC-s) that govern weak oscillator coupling; (iv) show isochron curvature, and recover nonlinear features of isochron geometry. Our method may find application wherever models of oscillator dynamics need to be constructed from measured or simulated time-series.