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arXiv · 2111.06511

Phase Response Curves and the Role of Coordinates

Simon Wilshin·Matthew D. Kvalheim·Shai Revzen
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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 $y\in\mathbb{R}$ actually depends on the full choice of coordinates $(x,y)$, $x\in\mathbb{R}^d$. 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.

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Simon Wilshin, Matthew D. Kvalheim, Shai Revzen. 2021-11-12. Phase Response Curves and the Role of Coordinates. https://arxiv.org/abs/2111.06511

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