Inferring the phase response curve from observation of a continuously perturbed oscillator

Cestnik, Rok; Rosenblum, Michael G.

doi:10.1038/s41598-018-32069-y

Cited by 22 publications

(16 citation statements)

References 28 publications

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“…Sawtooth-shaped PRCs are observed in a number of systems with oscillatory dynamics, including the van der Pol oscillator ( Cestnik and Rosenblum, 2018 ), and may reflect a phase resetting property of an oscillator with respect to a perturbation ( Izhikevich, 2007 ; Schultheiss et al, 2011 ). Further interpretation of the PRC results is given below.…”

Section: Resultsmentioning

confidence: 99%

Phase response analyses support a relaxation oscillator model of locomotor rhythm generation in Caenorhabditis elegans

Fouad

Teng

et al. 2021

eLife

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Neural circuits coordinate with muscles and sensory feedback to generate motor behaviors appropriate to an animal’s environment. In C. elegans, the mechanisms by which the motor circuit generates undulations and modulates them based on the environment are largely unclear. We quantitatively analyzed C. elegans locomotion during free movement and during transient optogenetic muscle inhibition. Undulatory movements were highly asymmetrical with respect to the duration of bending and unbending during each cycle. Phase response curves induced by brief optogenetic inhibition of head muscles showed gradual increases and rapid decreases as a function of phase at which the perturbation was applied. A relaxation oscillator model based on proprioceptive thresholds that switch the active muscle moment was developed and is shown to quantitatively agree with data from free movement, phase responses, and previous results for gait adaptation to mechanical loadings. Our results suggest a neuromuscular mechanism underlying C. elegans motor pattern generation within a compact circuit.

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Section: Resultsmentioning

confidence: 99%

Phase response analyses support a relaxation oscillator model of locomotor rhythm generation in Caenorhabditis elegans

Fouad

Teng

et al. 2021

eLife

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“…This starting point is born out of independent work presented in part 1 [1]. The approximate functional form of these phase response curves of perturbed oscillators often fall into two camps 1) always positive, or 2) a crossover from negative to positive [59]. In this work, we present our efforts to understand the collective dynamics of force mediated phase oscillators coupled by phase response curves of the second type.…”

Section: B Flocking Ciliary Oscillators (Aka Swarmalators)mentioning

confidence: 99%

Ciliary flocking and emergent instabilities enable collective agility in a non-neuromuscular animal

Bull,

Prakash,

Prakash

2021

Preprint

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Effective organismal behavior is characterized by the ability to respond appropriately to changes in the surrounding environment. Attaining this delicate balance of sensitivity and stability is a hallmark of the animal kingdom. By studying the locomotory behavior of a simple animal (Trichoplax adhaerens) without muscles or neurons, here we demonstrate how monociliated epithelial cells work collectively to give rise to an agile non-neuromuscular organism. Via direct visualization of large ciliary arrays, we report the discovery of sub-second ciliary reorientations under a rotational torque that is mediated by collective tissue mechanics and the adhesion of cilia to the underlying substrate.In an illuminating toy model, we show a mapping of this system onto an "active-elastic resonator". This framework explains how perturbations propagate information in this array as linear speed traveling waves in response to mechanical stimulus. Next, we explore the implications of periodic and noisy parametric driving in this active-elastic resonator and show that such driving can excite mechanical 'spikes'. These spikes in collective mode amplitudes are consistent with a system driven by parametric amplification and a saturating nonlinearity. We conduct extensive numerical experiments to corroborate these findings within a polarized active-elastic sheet. These results indicate that periodic and stochastic forcing are critical for increasing the sensitivity of collective ciliary flocking. We support these theoretical predictions via direct experimental observation of linear speed traveling waves which are made possible through the hybridization of spin and overdamped density waves. We map how these ciliary flocking dynamics result in agile motility via coupling between an amplified resonator and a tuning (Goldstone-like) mode of the system. This sets the stage for how activity and elasticity can self-organize into behavior which benefits the organism as a whole.

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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%

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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Inferring the phase response curve from observation of a continuously perturbed oscillator

Cited by 22 publications

References 28 publications

Phase response analyses support a relaxation oscillator model of locomotor rhythm generation in Caenorhabditis elegans

Phase response analyses support a relaxation oscillator model of locomotor rhythm generation in Caenorhabditis elegans

Ciliary flocking and emergent instabilities enable collective agility in a non-neuromuscular animal

A practical method for estimating coupling functions in complex dynamical systems

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