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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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Process of phasegram generation. (a) Spectrogram of a signal synthesized from the logistic map (see text). (b) Time-domain signal of x[i]. (c) Three portions of the signal, extracted at times t = 1.35, t = 4.9 and t = 8.57 s. (d) Phase portraits from the above signals, created by attractor reconstruction. A Poincaré section was created along the x-axis (orange), yielding intersection points with the trajectory (red dots). (e) Histograms of trajectory intersection points with Poincaré sections for all three extracted signal portions. For better visibility, a very large histogram bin width of 0.025 was chosen. (f) ‘Trajectory strips’: colour-coded histograms of Poincaré sections through phase portraits (see text); (g) phasegram from the signal displayed in (a) and (b). The markers at t = 1.35, t = 4.9 and t = 8.57 s represent the position of the three trajectory strips from (f) within the graph.
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RSIF20130288F2: Process of phasegram generation. (a) Spectrogram of a signal synthesized from the logistic map (see text). (b) Time-domain signal of x[i]. (c) Three portions of the signal, extracted at times t = 1.35, t = 4.9 and t = 8.57 s. (d) Phase portraits from the above signals, created by attractor reconstruction. A Poincaré section was created along the x-axis (orange), yielding intersection points with the trajectory (red dots). (e) Histograms of trajectory intersection points with Poincaré sections for all three extracted signal portions. For better visibility, a very large histogram bin width of 0.025 was chosen. (f) ‘Trajectory strips’: colour-coded histograms of Poincaré sections through phase portraits (see text); (g) phasegram from the signal displayed in (a) and (b). The markers at t = 1.35, t = 4.9 and t = 8.57 s represent the position of the three trajectory strips from (f) within the graph.

Mentions: The phasegram generation process is analogous to creating electroglottographic (EGG) wavegrams, a method previously developed by Herbst et al. [11]. Phasegram generation is outlined below (see also figure 2), and will be described in more detail in the following paragraphs.


Visualization of system dynamics using phasegrams.

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

Process of phasegram generation. (a) Spectrogram of a signal synthesized from the logistic map (see text). (b) Time-domain signal of x[i]. (c) Three portions of the signal, extracted at times t = 1.35, t = 4.9 and t = 8.57 s. (d) Phase portraits from the above signals, created by attractor reconstruction. A Poincaré section was created along the x-axis (orange), yielding intersection points with the trajectory (red dots). (e) Histograms of trajectory intersection points with Poincaré sections for all three extracted signal portions. For better visibility, a very large histogram bin width of 0.025 was chosen. (f) ‘Trajectory strips’: colour-coded histograms of Poincaré sections through phase portraits (see text); (g) phasegram from the signal displayed in (a) and (b). The markers at t = 1.35, t = 4.9 and t = 8.57 s represent the position of the three trajectory strips from (f) within the graph.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

RSIF20130288F2: Process of phasegram generation. (a) Spectrogram of a signal synthesized from the logistic map (see text). (b) Time-domain signal of x[i]. (c) Three portions of the signal, extracted at times t = 1.35, t = 4.9 and t = 8.57 s. (d) Phase portraits from the above signals, created by attractor reconstruction. A Poincaré section was created along the x-axis (orange), yielding intersection points with the trajectory (red dots). (e) Histograms of trajectory intersection points with Poincaré sections for all three extracted signal portions. For better visibility, a very large histogram bin width of 0.025 was chosen. (f) ‘Trajectory strips’: colour-coded histograms of Poincaré sections through phase portraits (see text); (g) phasegram from the signal displayed in (a) and (b). The markers at t = 1.35, t = 4.9 and t = 8.57 s represent the position of the three trajectory strips from (f) within the graph.
Mentions: The phasegram generation process is analogous to creating electroglottographic (EGG) wavegrams, a method previously developed by Herbst et al. [11]. Phasegram generation is outlined below (see also figure 2), and will be described in more detail in the following paragraphs.

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