Inferring oscillator's phase and amplitude response from a scalar signal exploiting test stimulation

TL;DR

This paper introduces a novel method called IPID-1 for inferring phase and amplitude response curves of oscillators from scalar signals, applicable to noisy, high-dimensional, and arbitrarily shaped stimuli, with significant implications for neuroscience.

Contribution

The paper presents a new technique, IPID-1, for directly reconstructing phase and amplitude responses from scalar signals, improving inference accuracy in complex and noisy systems.

Findings

IPID-1 outperforms existing methods in noisy and high-dimensional scenarios.

The technique works with stimuli of arbitrary shape, including charge-balanced pulses.

An error measure for assessing inference quality is introduced.

Abstract

The phase sensitivity curve or phase response curve (PRC) quantifies the oscillator's reaction to stimulation at a specific phase and is a primary characteristic of a self-sustained oscillatory unit. Knowledge of this curve yields a phase dynamics description of the oscillator for arbitrary weak forcing. Similar, though much less studied characteristic, is the amplitude response that can be defined either using an ad hoc approach to amplitude estimation or via the isostable variables. Here, we discuss the problem of the phase and amplitude response inference from observations using test stimulation. Although PRC determination for noise-free neuronal-like oscillators perturbed by narrow pulses is a well-known task, the general case remains a challenging problem. Even more challenging is the inference of the amplitude response. This characteristic is crucial, e.g., for controlling the amplitude of the collective mode in a network of interacting units -- a task relevant to neuroscience. Here, we compare the performance of different techniques suitable for inferring the phase and amplitude response, particularly with application to macroscopic oscillators. We suggest improvements to these techniques, e.g., demonstrating how to obtain the PRC in case of stimuli of arbitrary shape. Our main result is a novel technique denoted by IPID-1, based on the direct reconstruction of the Winfree equation and the analogous first-order equation for isostable dynamics. The technique works for signals with or without well-pronounced marker events and pulses of arbitrary shape; in particular, we consider charge-balanced pulses typical in neuroscience applications. Moreover, this technique is superior for noisy and high-dimensional systems. Additionally, we describe an error measure that can be computed solely from data and complements any inference technique.