Phase Response Curves and the Role of Coordinates

Simon Wilshin, Matthew D Kvalheim, Shai Revzen

arXiv preprint, 2021

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∈\R^d. 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.

BibTeX

@unpublished{wilshin2021phase,
  author = {Wilshin, Simon and Kvalheim, Matthew D and Revzen, Shai},
  title = {Phase Response Curves and the Role of Coordinates},
  year = {2021},
  cvtopic = {ddmodel},
  eprint = {2111.06511},
  doi = {10.48550/arXiv.2111.06511},
  eprinttype = {arxiv},
  journal = {arXiv preprint},
}