Phase Response Curves and the Role of Coordinates

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2111.06511.pdf (16.27 MB)

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https://arxiv.org/abs/2111.06511

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https://doi.org/10.48550/arXiv.2111.06511
 http://hdl.handle.net/11603/30371

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UMBC Mathematics and Statistics Department

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

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2012-11-12

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journal articles
preprints
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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 ∈ 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.