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. 2017 Aug;14(133):20170002.
doi: 10.1098/rsif.2017.0002.

Controllable Biomimetic Birdsong

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Free PMC article

Controllable Biomimetic Birdsong

Aryesh Mukherjee et al. J R Soc Interface. .
Free PMC article

Abstract

Birdsong is the product of the controlled generation of sound embodied in a neuromotor system. From a biophysical perspective, a natural question is that of the difficulty of producing birdsong. To address this, we built a biomimetic syrinx consisting of a stretched simple rubber tube through which air is blown, subject to localized mechanical squeezing with a linear actuator. A large static tension on the tube and small dynamic variations in the localized squeezing allow us to control transitions between three states: a quiescent state, a periodic state and a solitary wave state. The static load brings the system close to threshold for spontaneous oscillations, while small dynamic loads allow for rapid transitions between the states. We use this to mimic a variety of birdsongs via the slow-fast modulated nonlinear dynamics of the physical substrate, the syrinx, regulated by a simple controller. Finally, a minimal mathematical model of the system inspired by our observations allows us to address the problem of song mimicry in an excitable oscillator for tonal songs.

Keywords: biomimetics; birdsong.

Conflict of interest statement

We declare we have no competing interests.

Figures

Figure 1.
Figure 1.
A bird syrinx, its biomimetic analogue, and the dynamics of the device. (a) Schematic of a zebra finch syrinx. S is the sound box (syrinx) of the bird, U is airflow coming from the lungs, A–F is the acoustic filter formed by the oropharyngeal–oesophageal cavity, beak and trachea [29], M denotes muscular action along the length of the bronchus. (b) Schematic of experimental set-up. s1, Tx, strain gauge and stage to control lateral tension; s2, Ty, gauge and stage to control longitudinal tension; U, flowmeter; g, grid projected onto device. Inset (on right) shows side view of the set-up. L, 10 mW Green laser pointer; m, mask used to produce grid; p, probe used to actuate device; c, high-speed video camera (up to 90 kHz frame rate). The probe p is a linear motor to excite the membrane by pushing anywhere along its length, and mimics muscular actuation along the length of the bronchus. An image of the actual device is shown on the left. (c)(i)–(iii) Demonstration of the principle of the optical reconstruction. (i) shows the top surface of the device, described by the function z(x, y), being impinged by pencils of laser light described by the functions zn(x, y), where the index n characterizes the raster location. The light is incident on the device at an angle θ and the dashed lines show the intended path of the laser before it is intercepted by the surface. (ii),(iii) Images of the raw data with the flow turned off and on, respectively. The distance that each point in (c)(iii) has moved from its original location in (c)(ii) is proportional to the height at the observed point and this information can be used to reconstruct the entire surface in three dimensions. (d) The phase space of a device as a function of flow velocity U and probe depth d measured relative to the first depth (100 μm) at which sound is produced. Note that the solitary regime may have further subharmonic bifurcations A ‘mixed’ phase between chaotic and solitary also exists, marked in black in the phase space. (e) Digitized kymograph (positive y-direction corresponds to, height h(t) of the membrane at a point y = 0.5 cm from the mouth, and sound pressure level (spl) for the three regimes: tonal, aperiodic and solitary. (Online version in colour.)
Figure 2.
Figure 2.
Controllable transitions in a biomimetic syrinx. (ac) Dynamic action of probe. (a)(i) and (b)(i) The spectrograms of two complicated sounds created by dynamically controlling the probe. The probe is programmed with a pulse sequence to create the sounds (we specify the position and acceleration). (a)(ii) and (b)(ii) The position of the probe, relative to the spectrogram of the sound created. (c)(i)–(iii) The sound pressure levels for the sections indicated in (b)(ii). (c)(i) Sinusoidal, (ii) oscillations following a period-doubling transition, and (iii) chaotic sound. We see that by actuating the probe, we can change the qualitative nature of sound production. (df) Spectrograms of real and mimicked bird songs (using dynamic action of the probe). (d)(i) A song from a red-eyed vireo, and (d)(ii) songs mimicked by dynamical control of the device. The vireo has beautiful tonal songs with rapid and large variations in frequency. The device was operated in the tonal regime and reproduces songs well when the variation in frequency is not very large. (e)(i) A real and (e)(ii) mimicked song from a bengalese finch. These songs consisted of short harmonic pulses, which were well reproduced by the device. Even subtle frequency changes and transitions to a period doubled mode were well captured. (f)(i) A real and (f)(ii) mimicked song from a zebra finch. These songs show large spectral variation as well as high harmonic content and are difficult to reproduce. However, given the limitations of the linear motor, many features of the zebra finch song (large changes in frequency, transitions to chaos, high harmonic content) can be qualitatively reproduced. (Online version in colour.)
Figure 3.
Figure 3.
Mimicking a tonal song of the red-eyed vireo using a minimal model described in §3. (a) Spectrogram of a song of a red-eyed vireo: (i) original and (ii) computational mimic (see text). (b)(i) Time trace of the amplitude of the amplitude of the center frequency of the tonal song for the actual birdsong (blue) and its computational mimic (red) lie essentially on top of each other. (ii) The solution of the optimization problem (3.2) shows the temporal evolution of the damping r(t) (left abscissa) and the frequency ω(t) (right abscissa). (Online version in colour.)

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