Estimating Phase from Observed Trajectories Using the Temporal 1-Form
| dc.contributor.author | Wilshin, Simon | |
| dc.contributor.author | Kvalheim, Matthew D. | |
| dc.contributor.author | Scott, Clayton | |
| dc.contributor.author | Revzen, Shai | |
| dc.date.accessioned | 2023-10-25T14:29:38Z | |
| dc.date.available | 2023-10-25T14:29:38Z | |
| dc.date.issued | 2022-03-09 | |
| dc.description.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. | en_US |
| dc.description.sponsorship | We are deeply indebted to John M. Guckenheimer for conceiving of the Temporal 1-Form and providing guidance and comments. We also thank Dan Guralnik and G. Bard Ermentrout for valuable insights. This work was supported by supported by EPSRC grant EP/H04924X/1, BBSRC grant BB/J021504/1, and U. S. Army Research Office under contract/grant number 64929EG supporting S. Wilshin, ARO W911NF-18-1-0327 and ONR N000141612817 (held by D. E. Koditschek) supporting M. D. Kvalheim, NSF Grants 1422157 and 1838179 to C. Scott, and ARO Young Investigator Award #61770 and W911NF-14-1-0573 to S. Revzen. The guineafowl kinematics were gathered under the supervision of M. Daley with the support of a Human Frontier Science Program grant (RGY0062/2010) and ethical approval was obtained from Royal Veterinary College Ethics and Welfare Committee under the protocol title, “Kinematics and kinetics in birds running over uneven terrain”. The optical transmission data for the Belousov-Zhabotinsky reaction were obtained from S. Fraden and M. Norton of Brandeis University, under awards from the National Science Foundation NSF DMREF-1534890 and U. S. Army Research Laboratory and U. S. Army Research Office W911NF-16-1-0094. | en_US |
| dc.description.uri | https://arxiv.org/abs/2203.04498 | en_US |
| dc.format.extent | 23 pages | en_US |
| dc.genre | journal articles | en_US |
| dc.genre | preprints | en_US |
| dc.identifier | doi:10.13016/m2ajjn-vztd | |
| dc.identifier.uri | https://doi.org/10.48550/arXiv.2203.04498 | |
| dc.identifier.uri | http://hdl.handle.net/11603/30370 | |
| dc.language.iso | en_US | en_US |
| dc.relation.isAvailableAt | The University of Maryland, Baltimore County (UMBC) | |
| dc.relation.ispartof | UMBC Mathematics Department Collection | |
| dc.rights | This item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author. | en_US |
| dc.title | Estimating Phase from Observed Trajectories Using the Temporal 1-Form | en_US |
| dc.type | Text | en_US |
| dcterms.creator | https://orcid.org/0000-0002-2662-6760 | en_US |