Inferring oscillator's phase and amplitude response from a scalar signal exploiting test stimulation
- 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 differentThe 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.…
Author details: | Rok CestnikORCiDGND, Erik T. K. MauORCiD, Michael RosenblumORCiDGND |
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DOI: | https://doi.org/10.1088/1367-2630/aca70a |
ISSN: | 1367-2630 |
Title of parent work (English): | New journal of physics : the open-access journal for physics |
Publisher: | Dt. Physikalische Ges., IOP |
Place of publishing: | Bad Honnef, London |
Publication type: | Article |
Language: | English |
Date of first publication: | 2022/12/14 |
Publication year: | 2022 |
Release date: | 2024/07/26 |
Tag: | amplitude response; inference; phase response; phase-isostable reduction |
Volume: | 24 |
Issue: | 12 |
Article number: | 123012 |
Number of pages: | 27 |
Funding institution: | Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) [PI; 220/21-1, 424778381 - TRR 295] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
Peer review: | Referiert |
Publishing method: | Open Access / Gold Open-Access |
DOAJ gelistet | |
License (German): | ![]() |