Dynamics in the Sakaguchi-Kuramoto model with bimodal frequency distribution

Guo, Shuangjian; Xie, Yuan; Dai, Qionglin; Li, Haihong; Yang, Junzhong

doi:10.1371/journal.pone.0243196

Cited by 3 publications

(4 citation statements)

References 40 publications

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“…As the drift-pitchfork line does not involve any attractors we did not made more efforts to trace it completely. In analogy to the result in 36 , we expected this line to bend backwards and terminate at the origin. The presence of a drift-pitchfork bifurcation confirms that the TB point fully consistent with the O(2) symmetry of the model: invariance under rotation θ → θ + c and reflection Ω → −Ω.…”

Section: Please Cite This Article Asmentioning

confidence: 84%

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Efficient moment-based approach to the simulation of infinitely many heterogeneous phase oscillators

León

Pazó

2022

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The dynamics of ensembles of phase oscillators are usually described considering their infinite-size limit. In practice, however, this limit is fully accessible only if the Ott–Antonsen theory can be applied, and the heterogeneity is distributed following a rational function. In this work, we demonstrate the usefulness of a moment-based scheme to reproduce the dynamics of infinitely many oscillators. Our analysis is particularized for Gaussian heterogeneities, leading to a Fourier–Hermite decomposition of the oscillator density. The Fourier–Hermite moments obey a set of hierarchical ordinary differential equations. As a preliminary experiment, the effects of truncating the moment system and implementing different closures are tested in the analytically solvable Kuramoto model. The moment-based approach proves to be much more efficient than the direct simulation of a large oscillator ensemble. The convenience of the moment-based approach is exploited in two illustrative examples: (i) the Kuramoto model with bimodal frequency distribution, and (ii) the “enlarged Kuramoto model” (endowed with nonpairwise interactions). In both systems, we obtain new results inaccessible through direct numerical integration of populations.

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Section: Please Cite This Article Asmentioning

confidence: 84%

“…With the advent of the Ott-Antonsen theory, the problem became (almost) fully solvable for frequency distributions of rational type, see e.g. [33][34][35][36] . Instead, we consider here a distribution equal to the sum of two normal distributions centered at ±Ω 0 and variance σ 2 .…”

Section: Kuramoto Model With Bimodal Distributionmentioning

confidence: 99%

Efficient moment-based approach to the simulation of infinitely many heterogeneous phase oscillators

León

Pazó

2022

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…In terms of parameter interpretations, we provide a brief summary based on previous work (Hannay et al, 2019;St Hilaire et al, 2007;Hannay, n.d.;Kronauer et al, 1999). In particular, the parameter τ is the intrinsic circadian period, typically close to 24 h in duration when the shear parameter β 1 0 = (Guo et al, 2020;Montbrió and Pazó, 2011). For β 1 nonzero, the period of the oscillator is also amplitudedependent.…”

Section: Methodsmentioning

confidence: 99%

“…; Kronauer et al, 1999). In particular, the parameter τ is the intrinsic circadian period, typically close to 24 h in duration when the shear parameter β 1 = 0 (Guo et al, 2020; Montbrió and Pazó, 2011). For β 1 nonzero, the period of the oscillator is also amplitude-dependent. K represents the averaged coupling strength between oscillators in the SCN; γ controls the dispersion of the natural frequencies of the oscillators; D represents the noise strength (set to zero here); A 1 A 2 β L 1 β L 2 and σ determine the form of the phase response curve of neurons to light pulses and the entrainment angle of the model; G is a scaling factor for the light drive onto the circadian pacemaker; …”

Section: Methodsmentioning

confidence: 99%

Impact of Light Schedules and Model Parameters on the Circadian Outcomes of Individuals

et al. 2023

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Key differences exist between individuals in terms of certain circadian-related parameters, such as intrinsic period and sensitivity to light. These variations can differentially impact circadian timing, leading to challenges in accurately implementing time-sensitive interventions. In this work, we parse out these effects by investigating the impact of parameters from a macroscopic model of human circadian rhythms on phase and amplitude outputs. Using in silico light data designed to mimic commonly studied schedules, we assess the impact of parameter variations on model outputs to gain insight into the different effects of these schedules. We show that parameter sensitivity is heavily modulated by the lighting routine that a person follows, with darkness and shift work schedules being the most sensitive. We develop a framework to measure overall sensitivity levels of the given light schedule and furthermore decompose the overall sensitivity into individual parameter contributions. Finally, we measure the ability of the model to extract parameters given light schedules with noise and show that key parameters like the circadian period can typically be recovered given known light history. This can inform future work on determining the key parameters to consider when personalizing a model and the lighting protocols to use when assessing interindividual variability.

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Efficient moment-based approach to the simulation of infinitely many heterogeneous phase oscillators

León,

Pazó

2022

Preprint

View full text Add to dashboard Cite

The dynamics of ensembles of phase oscillators are usually described considering their infinite-size limit. In practice, however, this limit is fully accessible only if the Ott-Antonsen theory can be applied, and the heterogeneity is distributed following a rational function. In this work we demonstrate the usefulness of a moment-based scheme to reproduce the dynamics of infinitely many oscillators. Our analysis is particularized for Gaussian heterogeneities, leading to a Fourier-Hermite decomposition of the oscillator density. The Fourier-Hermite moments obey a set of hierarchical ordinary differential equations. As a preliminary experiment, the effects of truncating the moment system and implementing different closures are tested in the analytically solvable Kuramoto model. The moment-based approach proves to be much more efficient than the direct simulation of a large oscillator ensemble. The convenience of the moment-based approach is exploited in two illustrative examples: (i) the Kuramoto model with bimodal frequency distribution, and (ii) the 'enlarged Kuramoto model' (endowed with nonpairwise interactions). In both systems we obtain new results inaccessible through direct numerical integration of populations.

show abstract

Dynamics in the Sakaguchi-Kuramoto model with bimodal frequency distribution

Cited by 3 publications

References 40 publications

Efficient moment-based approach to the simulation of infinitely many heterogeneous phase oscillators

Efficient moment-based approach to the simulation of infinitely many heterogeneous phase oscillators

Impact of Light Schedules and Model Parameters on the Circadian Outcomes of Individuals

Efficient moment-based approach to the simulation of infinitely many heterogeneous phase oscillators

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