Phase Response Curves and the Role of Coordinates
| dc.contributor.author | Wilshin, Simon | |
| dc.contributor.author | Kvalheim, Matthew D. | |
| dc.contributor.author | Revzen, Shai | |
| dc.date.accessioned | 2023-10-25T14:41:07Z | |
| dc.date.available | 2023-10-25T14:41:07Z | |
| dc.date.issued | 2012-11-12 | |
| dc.description.abstract | The "Phase Response Curve" (PRC) is a common tool used to analyze phase resetting in the natural sciences. We make the observation that the PRC with respect to a coordinate y ∈ ℝ actually depends on the full choice of coordinates (x,y), x ∈ ℝᵈ. We give a coordinate-free definition of the PRC making this observation obvious. We show how by controlling y, using delay coordinates of y, and postulating the dynamics of x as a function of x and y, we can sometimes reconstruct the PRC with respect to the (x,y) coordinates. This suggests a means for obtaining the PRC of, e.g., a neuron via a voltage clamp. | en_US |
| dc.description.sponsorship | Kvalheim was supported in part by the Army Research Office (ARO) under the SLICE Multidisciplinary University Research Initiatives (MURI) Program, award W911NF18-1-0327, and in part by ONR N000141612817, a Vannevar Bush Faculty Fellowship held by Daniel E. Koditschek, sponsored by the Basic Research Office of the Assistant Secretary of Defense for Research and Engineering. Revzen was supported by ARO W911NF-14-1-0573, ARO MURI W911NF-17-1-0306, NSF CMMI 1825918, and the D. Dan and Betty Kahn Michigan-Israel Partnership for Research and Education. | en_US |
| dc.description.uri | https://arxiv.org/abs/2111.06511 | en_US |
| dc.format.extent | 21 pages | en_US |
| dc.genre | journal articles | en_US |
| dc.genre | preprints | en_US |
| dc.identifier | doi:10.13016/m2kwxa-0osx | |
| dc.identifier.uri | https://doi.org/10.48550/arXiv.2111.06511 | |
| dc.identifier.uri | http://hdl.handle.net/11603/30371 | |
| 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 | Phase Response Curves and the Role of Coordinates | en_US |
| dc.type | Text | en_US |
| dcterms.creator | https://orcid.org/0000-0002-2662-6760 | en_US |