Reconstructing bifurcation diagrams only from time-waveforms

Tokunaga, Ryuji; Kajiwara, Shihoko; Matsumoto, Takashi

doi:10.1016/0167-2789(94)90092-2

Cited by 7 publications

(3 citation statements)

References 15 publications

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“…Next, eigenvalues and eigenvectors are obtained from the results of applying principal component analysis to [Δβ (1) Δβ (2) • • • Δβ (N ) ], where Δβ (n) is a deviation vector of β (n) as follows:…”

Section: Reconstruction Of Bifurcation Diagramsmentioning

confidence: 99%

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Reconstructing one- and two-bifurcation diagrams of all components in the Rössler equations only from time-series data sets

Itoh

Adachi

2021

NOLTA

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We reconstruct bifurcation diagrams of all components in the Rössler equations only from time-series data sets, thereby estimating the attractors when the parameter values are changed. In this study, we show that the bifurcation diagrams of all components can be reconstructed from time-series data of all components. In addition, we estimate the Lyapunov spectrum of the reconstructed bifurcation diagrams. We expect that the reconstruction requires a shorter length of training data when using time-series data sets of all components compared with one component. Accordingly, in numerical experiments, we reconstruct the bifurcation diagrams using training data whose length is shorter than when a bifurcation diagram is reconstructed using training data of one component.

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Section: Reconstruction Of Bifurcation Diagramsmentioning

confidence: 99%

“…In 1994, Tokunaga et al proposed a method for reconstructing bifurcation diagrams (BDs) [1] that several research groups then studied [2][3][4][5][6][7][8][9][10]. BD reconstruction allows attractors to be estimated when the bifurcation parameter values of a target system are changed.…”

Section: Introductionmentioning

confidence: 99%

Reconstructing one- and two-bifurcation diagrams of all components in the Rössler equations only from time-series data sets

Itoh

Adachi

2021

NOLTA

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“…The time-series prediction problem has been studied by many researchers using various techniques, such as neural networks and learning algorithms. Tokunaga et al has proposed the reconstruction of BDs from only time-series data [1]. In conventional time-series prediction, no dynamical system parameters are estimated.…”

Section: Introductionmentioning

confidence: 99%

Reconstructing bifurcation diagrams with Lyapunov exponents from only time-series data using an extreme learning machine

Itoh

Tada

Adachi

2017

NOLTA

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Abstract:We describe a method for reconstructing bifurcation diagrams with Lyapunov exponents for chaotic systems using only time-series data. The reconstruction of bifurcation diagrams is a problem of time-series prediction and predicts oscillatory patterns of time-series data when parameters change. Therefore, we expect the reconstruction of bifurcation diagram could be used for real-world systems that have variable environmental factors, such as temperature, pressure, and concentration. In the conventional method, the accuracy of the reconstruction can be evaluated only qualitatively. In this paper, we estimate Lyapunov exponents for reconstructed bifurcation diagrams so that we can quantitatively evaluate the reconstruction. We also present the results of numerical experiments that confirm that the features of the reconstructed bifurcation diagrams coincide with those of the original ones.

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Bifurcations and chaos in register transitions of excised larynx experiments

Tokuda

Horáček

Švec

et al. 2008

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Experimental data from an excised larynx are analyzed in the light of nonlinear dynamics. The excised larynx provides an experimental framework that enables artificial control and direct observation of the vocal fold vibrations. Of particular interest in this experiment is the coexistence of two distinct vibration patterns, which closely resemble chest and falsetto registers of the human voice. Abrupt transitions between the two registers are typically accompanied by irregular vibrations. Two approaches are presented for the modeling of the excised larynx experiment; one is the nonlinear predictive modeling of the experimental time series and the other is the biomechanical modeling (three-mass model) that takes into account basic mechanisms of the vocal fold vibrations. The two approaches show that the chest and falsetto vibrations correspond to two coexisting limit cycles, which jump to each other with a change in the bifurcation parameter. Irregular vibrations observed at the register jumps are due to chaos that exists near the two limit cycles. This provides an alternative mechanism to generate chaotic vibrations in excised larynx experiment, which is different from the conventionally known mechanisms such as strong asymmetry between the left and right vocal folds or excessively high subglottal pressure.

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Reconstructing bifurcation diagrams only from time-waveforms

Cited by 7 publications

References 15 publications

Reconstructing one- and two-bifurcation diagrams of all components in the Rössler equations only from time-series data sets

Reconstructing one- and two-bifurcation diagrams of all components in the Rössler equations only from time-series data sets

Reconstructing bifurcation diagrams with Lyapunov exponents from only time-series data using an extreme learning machine

Bifurcations and chaos in register transitions of excised larynx experiments

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