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Detecting synchronizations in an asymmetric vocal fold model from time series data
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10.1063/1.1848232
/content/aip/journal/chaos/15/1/10.1063/1.1848232
http://aip.metastore.ingenta.com/content/aip/journal/chaos/15/1/10.1063/1.1848232

Figures

Image of FIG. 1.
FIG. 1.

Schematic representation of the asymmetric two mass model of the vocal folds. Each vocal fold is approximated by two coupled oscillators of masses and . Springs and and dampers and represent the viscoelastic properties of vocal fold tissue.

Image of FIG. 2.
FIG. 2.

Bifurcation diagrams of the asymmetric vocal system (top) and its reconstruction (bottom). The subglottal pressure is fixed at . The horizontal axis corresponds to the asymmetry parameter and the vertical axis represents local maxima of the right vocal fold . For the asymmetric vocal system, the first Lyapunov exponent is drawn (middle), where the regime of chaos with a positive exponent appears in .

Image of FIG. 3.
FIG. 3.

Bifurcation diagrams of the asymmetric vocal system (top) and its reconstruction (bottom). The diagrams of Fig. 2 are extended to a larger range of the asymmetry parameter .

Image of FIG. 4.
FIG. 4.

Locations of the three sets of the model parameters in a two-dimensional principal component space. The new coordinates, and , correspond to the asymmetry parameter and the subglottal pressure .

Image of FIG. 5.
FIG. 5.

Synchronization diagram of the asymmetric vocal system (top) and its reconstruction (bottom). The subglottal pressure is fixed at . The horizontal line corresponds to the asymmetry parameter and the vertical line corresponds to the frequency ratio between the right and the left vocal folds.

Image of FIG. 6.
FIG. 6.

Synchronization diagram of the asymmetric vocal system (top) and its reconstruction (bottom). Dependence of the frequency ratio on the asymmetry parameter and the subglottal pressure is drawn in the range of .

Image of FIG. 7.
FIG. 7.

Borderlines between regimes of normal phonation (1:1 synchronization) and abnormal phonation (synchronization other than 1:1 ratio or desynchronization) for the asymmetric vocal system (solid line) and its reconstruction (dotted line) in the range of .

Image of FIG. 8.
FIG. 8.

Regime of desynchronization (shaded circles) of the reconstructed model compared with the original, which is inside the borderline (thick solid line), in the range of . Regime of divergent solutions detected in the reconstructed model is indicated by crosses. (a): Case (b1), (b): Case (b2), (c): Case (b3), (d): Case (b4), (e): Case (c1), (f): Case (c2).

Tables

Generic image for table
Table I.

Sets of parameters used for the case studies and the correlation coefficients obtained to measure similarity between the original and the reconstructed synchronization diagram.

Generic image for table
Table II.

Parameter values used to generate a time series data and the type of their dynamics (limit cycle, torus, or chaos; synchronized, or desynchronized).

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/content/aip/journal/chaos/15/1/10.1063/1.1848232
2005-01-28
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Detecting synchronizations in an asymmetric vocal fold model from time series data
http://aip.metastore.ingenta.com/content/aip/journal/chaos/15/1/10.1063/1.1848232
10.1063/1.1848232
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