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Visualization of system dynamics using phasegrams.

Herbst CT, Herzel H, Svec JG, Wyman MT, Fitch WT - J R Soc Interface (2013)

Bottom Line: A phasegram can be interpreted as a bifurcation diagram in time.In contrast to other analysis techniques, it can be automatically constructed from time-series data alone: no additional system parameter needs to be known.Phasegrams show great potential for signal classification and can act as the quantitative basis for further analysis of oscillating systems in many scientific fields, such as physics (particularly acoustics), biology or medicine.

View Article: PubMed Central - PubMed

Affiliation: Department of Cognitive Biology, Laboratory of Bioacoustics, University of Vienna, Althanstrasse 14, 1090 Vienna, Austria. christian.herbst@univie.ac.at

ABSTRACT
A new tool for visualization and analysis of system dynamics is introduced: the phasegram. Its application is illustrated with both classical nonlinear systems (logistic map and Lorenz system) and with biological voice signals. Phasegrams combine the advantages of sliding-window analysis (such as the spectrogram) with well-established visualization techniques from the domain of nonlinear dynamics. In a phasegram, time is mapped onto the x-axis, and various vibratory regimes, such as periodic oscillation, subharmonics or chaos, are identified within the generated graph by the number and stability of horizontal lines. A phasegram can be interpreted as a bifurcation diagram in time. In contrast to other analysis techniques, it can be automatically constructed from time-series data alone: no additional system parameter needs to be known. Phasegrams show great potential for signal classification and can act as the quantitative basis for further analysis of oscillating systems in many scientific fields, such as physics (particularly acoustics), biology or medicine.

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Artificial phonation of an excised sika deer larynx produced during a pressure sweep (0–4.1–0 kPa). (a) Narrow-band spectrogram of the electroglottographic (EGG) signal; (b) EGG signal, extracted at t = 0.725, t = 2.3, t = 4 and t = 10 s. (c) Phase portraits from the above signals, created by plotting the real portion of the Hilbert-transformed EGG signal against its imaginary counterpart. A Poincaré section was created at an angle of 0.575 π radians, yielding intersection points with the trajectory (red dots). (d) Phasegram: the vertical markers at t = 0.48, t = 0.98, t = 3.18, t = 6.20, t = 13.14, t = 14.24, t = 15.59 and t = 16.07 s represent bifurcations, i.e. changes from distinct oscillatory regime to another (see text). (e) Trace of the time-varying air pressure: the vertical markers indicate bifurcation events (see above and text). (f) Bifurcation diagram, showing the distinct vibratory patterns in relation to air pressure. Note the hysteresis caused by the direction of air pressure change (increasing versus decreasing—see text for details).
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RSIF20130288F6: Artificial phonation of an excised sika deer larynx produced during a pressure sweep (0–4.1–0 kPa). (a) Narrow-band spectrogram of the electroglottographic (EGG) signal; (b) EGG signal, extracted at t = 0.725, t = 2.3, t = 4 and t = 10 s. (c) Phase portraits from the above signals, created by plotting the real portion of the Hilbert-transformed EGG signal against its imaginary counterpart. A Poincaré section was created at an angle of 0.575 π radians, yielding intersection points with the trajectory (red dots). (d) Phasegram: the vertical markers at t = 0.48, t = 0.98, t = 3.18, t = 6.20, t = 13.14, t = 14.24, t = 15.59 and t = 16.07 s represent bifurcations, i.e. changes from distinct oscillatory regime to another (see text). (e) Trace of the time-varying air pressure: the vertical markers indicate bifurcation events (see above and text). (f) Bifurcation diagram, showing the distinct vibratory patterns in relation to air pressure. Note the hysteresis caused by the direction of air pressure change (increasing versus decreasing—see text for details).

Mentions: Analysis of the EGG signal from excised sika deer larynx oscillations (figure 6a,b) revealed five distinct vibratory regimes: static (no oscillation; not displayed in figure 6b), periodic (small amplitude, gradual amplitude variation), irregular (complex non-periodic signal), period doubling and again periodic (stable at larger amplitude). These vibratory regimes can be readily distinguished from each other in the phasegram (table 2 and figure 6e).Table 2.


Visualization of system dynamics using phasegrams.

Herbst CT, Herzel H, Svec JG, Wyman MT, Fitch WT - J R Soc Interface (2013)

Artificial phonation of an excised sika deer larynx produced during a pressure sweep (0–4.1–0 kPa). (a) Narrow-band spectrogram of the electroglottographic (EGG) signal; (b) EGG signal, extracted at t = 0.725, t = 2.3, t = 4 and t = 10 s. (c) Phase portraits from the above signals, created by plotting the real portion of the Hilbert-transformed EGG signal against its imaginary counterpart. A Poincaré section was created at an angle of 0.575 π radians, yielding intersection points with the trajectory (red dots). (d) Phasegram: the vertical markers at t = 0.48, t = 0.98, t = 3.18, t = 6.20, t = 13.14, t = 14.24, t = 15.59 and t = 16.07 s represent bifurcations, i.e. changes from distinct oscillatory regime to another (see text). (e) Trace of the time-varying air pressure: the vertical markers indicate bifurcation events (see above and text). (f) Bifurcation diagram, showing the distinct vibratory patterns in relation to air pressure. Note the hysteresis caused by the direction of air pressure change (increasing versus decreasing—see text for details).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4043161&req=5

RSIF20130288F6: Artificial phonation of an excised sika deer larynx produced during a pressure sweep (0–4.1–0 kPa). (a) Narrow-band spectrogram of the electroglottographic (EGG) signal; (b) EGG signal, extracted at t = 0.725, t = 2.3, t = 4 and t = 10 s. (c) Phase portraits from the above signals, created by plotting the real portion of the Hilbert-transformed EGG signal against its imaginary counterpart. A Poincaré section was created at an angle of 0.575 π radians, yielding intersection points with the trajectory (red dots). (d) Phasegram: the vertical markers at t = 0.48, t = 0.98, t = 3.18, t = 6.20, t = 13.14, t = 14.24, t = 15.59 and t = 16.07 s represent bifurcations, i.e. changes from distinct oscillatory regime to another (see text). (e) Trace of the time-varying air pressure: the vertical markers indicate bifurcation events (see above and text). (f) Bifurcation diagram, showing the distinct vibratory patterns in relation to air pressure. Note the hysteresis caused by the direction of air pressure change (increasing versus decreasing—see text for details).
Mentions: Analysis of the EGG signal from excised sika deer larynx oscillations (figure 6a,b) revealed five distinct vibratory regimes: static (no oscillation; not displayed in figure 6b), periodic (small amplitude, gradual amplitude variation), irregular (complex non-periodic signal), period doubling and again periodic (stable at larger amplitude). These vibratory regimes can be readily distinguished from each other in the phasegram (table 2 and figure 6e).Table 2.

Bottom Line: A phasegram can be interpreted as a bifurcation diagram in time.In contrast to other analysis techniques, it can be automatically constructed from time-series data alone: no additional system parameter needs to be known.Phasegrams show great potential for signal classification and can act as the quantitative basis for further analysis of oscillating systems in many scientific fields, such as physics (particularly acoustics), biology or medicine.

View Article: PubMed Central - PubMed

Affiliation: Department of Cognitive Biology, Laboratory of Bioacoustics, University of Vienna, Althanstrasse 14, 1090 Vienna, Austria. christian.herbst@univie.ac.at

ABSTRACT
A new tool for visualization and analysis of system dynamics is introduced: the phasegram. Its application is illustrated with both classical nonlinear systems (logistic map and Lorenz system) and with biological voice signals. Phasegrams combine the advantages of sliding-window analysis (such as the spectrogram) with well-established visualization techniques from the domain of nonlinear dynamics. In a phasegram, time is mapped onto the x-axis, and various vibratory regimes, such as periodic oscillation, subharmonics or chaos, are identified within the generated graph by the number and stability of horizontal lines. A phasegram can be interpreted as a bifurcation diagram in time. In contrast to other analysis techniques, it can be automatically constructed from time-series data alone: no additional system parameter needs to be known. Phasegrams show great potential for signal classification and can act as the quantitative basis for further analysis of oscillating systems in many scientific fields, such as physics (particularly acoustics), biology or medicine.

Show MeSH
Related in: MedlinePlus