Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2017 Sep;27(9):092101.
doi: 10.1063/1.4986932.

Nonlinear dynamics in the study of birdsong

Gabriel B Mindlin  1
Affiliations

Nonlinear dynamics in the study of birdsong

Gabriel B Mindlin. Chaos. 2017 Sep.

Abstract

Birdsong, a rich and complex behavior, is a stellar model to understand a variety of biological problems, from motor control to learning. It also enables us to study how behavior emerges when a nervous system, a biomechanical device and the environment interact. In this review, I will show that many questions in the field can benefit from the approach of nonlinear dynamics, and how birdsong can inspire new directions for research in dynamics.

PubMed Disclaimer

Figures

FIG. 1.
FIG. 1.
The syrinx, the trachea and the oroesopharingeal cavity (a). Muscles controlling the oscine syrinx. See text for full description (b).
FIG. 2.
FIG. 2.
Isofrequencies in the parameter space of a simple model for labial dynamics. The slowly changing parameters during the production of a syllable are the coordinates of a trajectory in the parameter space. Pressure and tension are (β,k) in the model.
FIG. 3.
FIG. 3.
Experimental recordings during the production of a canary syllable. The sound (first panel), the air sac pressure (second panel), the electromyography of the right muscle syringealis ventralis (third panel) and the sonogram (fourth panel).
FIG. 4.
FIG. 4.
The modes of labia during one cycle.
FIG. 5.
FIG. 5.
Parameter space for the model described in the text. The red curves correspond to saddle node bifurcations and the blue curve to a Hopf (a). The sonogram of a recorded song (top panel) and the sonogram of a synthetic sound produced by the model (bottom panel) (b).
FIG. 6.
FIG. 6.
The relationship between the spectral content and the frequency for syllables, recorded from different birds. The continuous curve is obtained with our model: an oscillation born in a SNILC (saddle node in limit cycle), filtered with a tube.
FIG. 7.
FIG. 7.
A recorded song (top panel) and a synthetic sound (bottom panel) generated by the model described in the text.
FIG. 8.
FIG. 8.
Testing the response of highly selective neurons to synthetic sounds generated by the model, with slightly different parameters.
FIG. 9.
FIG. 9.
Asymmetric labia can generate sounds with distinctive timbre (notice the side bands in the sonograms). In the top panel is the bifurcation diagram. The recorded sonogram of the picazuro pigeon song and the synthetic sound generated with symmetric labia (left), compared with the song of maculosa pigeon and sound generated with asymmetric labia (right).
FIG. 10.
FIG. 10.
The spectrum of a song (first panel), synthetic sound with an added vortex sound (middle panel) and the synthetic sound without a vortex sound (bottom panel). There is a significant difference for frequencies higher than 10 kHz.
FIG. 11.
FIG. 11.
A schematic diagram of the nuclei in the oscine song system.
FIG. 12.
FIG. 12.
Recorded air sac pressure in a singing canary (a). A neural oscillator, i.e., a population of excitatory neurons coupled to a population of inhibitory ones (top). The bifurcation diagram showing the different regions of the parameter space presenting qualitatively different flows (bottom). The parameters are the inputs to the neural oscillator (b). The synthetic time series emulating air sac pressure (c). The syllables are generated changing the parameters along the trajectories displayed in (b).
FIG. 13.
FIG. 13.
One-way of generating synthetic pressure gestures similar to the recorded ones. The dynamical system is written in terms of the activities of interconnected nuclei.
FIG. 14.
FIG. 14.
Parameter space regions of the average model.
See this image and copyright information in PMC

References

    1. Neuroscience of Birdsong, edited by Zeigler H. P and Marler P. ( Cambridge University Press, Cambridge, 2008), pp. 5–31.
    1. Marler P., “ Birdsong and speech development: Could there be parallels? There may be basic rules governing vocal learning to which many species conform, including man,” Am. Sci. 58(6), 669–673 (1970). - PubMed
    1. Chiel H. J. and Beer R. D., “ The brain has a body: Adaptive behavior emerges from interactions of nervous system, body and environment,” Trends Neurosci. 20(12), 553–557 (1997). 10.1016/S0166-2236(97)01149-1 - DOI - PubMed
    1. Suthers R. A., Goller F., and Pytte C., “ The neuromuscular control of birdsong,” Philos. Trans. R. Soc. B: Biol. Sci. 354(1385), 927 (1999). 10.1098/rstb.1999.0444 - DOI - PMC - PubMed
    1. Schmidt M. F. and Goller F., “ Breathtaking songs: Coordinating the neural circuits for breathing and singing,” Physiology 31(6), 442–451 (2016). 10.1152/physiol.00004.2016 - DOI - PMC - PubMed

LinkOut - more resources