Acoustic measurements of the infinitesimal phase response curve from a sounding organ pipe

Okada, Masahiro; Kaburagi, Tokihiko; Tokuda, Isao T.

doi:10.1016/j.physleta.2019.02.034

Cited by 1 publication

(2 citation statements)

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“…The phase sensitivity function Z(θ) plays a vital role in the studies of coupled oscillators, since it describes one of the most fundamental properties of the oscillator element [58][59][60]. Numerous approaches have been proposed to estimate the phase sensitivity function from experimental data [43][44][45][46][47][48][49][50][51][52]. As an extension of our technique, the phase sensitivity function can be recovered from the coupling function [79].…”

Section: (A) Inferring Phase Sensitivity Functionmentioning

confidence: 99%

“…For a system of phase equations, a standard way to construct the coupling function is to measure phase sensitivity function of an individual oscillator element and obtain the coupling function by averaging method that computes the amount of phase shift induced through interaction with another oscillator element [42]. However, a precisely measured phase sensitivity function is not always accessible, since it requires application of external perturbations to an individual oscillator, which cannot always be isolated from the rest of the system [43][44][45][46][47][48][49][50][51][52].…”

Section: Introductionmentioning

confidence: 99%

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A practical method for estimating coupling functions in complex dynamical systems

Tokuda

Levnajić

Ishimura

2019

Phil. Trans. R. Soc. A.

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A foremost challenge in modern network science is the inverse problem of reconstruction (inference) of coupling equations and network topology from the measurements of the network dynamics. Of particular interest are the methods that can operate on real (empirical) data without interfering with the system. One of such earlier attempts [Tokuda et al., PRL, 2007] was a method suited for general limitcycle oscillators, yielding both oscillators' natural frequencies and coupling functions between them (phase equations) from empirically measured time series. The present paper reviews the above method in a way comprehensive to domain-scientists other than physics. It also presents applications of the method to (i) detection of the network connectivity, (ii) inference of the phase sensitivity function, (iii) approximation of the interaction among phase-coherent chaotic oscillators, (iv) experimental data from a forced Van der Pol electric circuit. This reaffirms the range of applicability of the method for reconstructing coupling functions and makes it accessible to a much wider scientific community.

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