Phase Response Curves and the Role of Coordinates

2021/11/12 by Wilshin, Simon, Kvalheim, Matthew D., Revzen, Shai
#34C15 #34C25 #37C27 #37N25 #92B25 #92C20 #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Biological sciences #FOS: Mathematics #Neurons and Cognition (q-bio.NC) #Optimization and Control (math.OC) #Quantitative Methods (q-bio.QM)

paper · doi:10.48550/arxiv.2111.06511

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.

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