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Mathematical physics

Mathematical physics

Physicists look at birdsong

17 Feb 2006 Belle Dumé

With spring on the way, physicists have turned their attention to the familiar sound of birdsong and have developed a mathematical model to explain the breathing patterns of canaries when they sing. By treating both a bird's vocal organ and neurones as nonlinear systems, researchers have found that complex songs, involving notes of many frequencies and lengths, might be produced by surprisingly simple neurological structures and processes. The results could shed light on how birds learn to sing and even how humans learn to speak -- a process thought to be similar to the mimicking behaviour of baby birds (Phys. Rev. Lett. 96 058103).

A bird’s vocal organ — or syrinx — is similar to the human larynx and consists of folds of tissue in the passage connecting the lungs to the vocal tract. When a bird exhales, the folds oscillate to produce notes with frequencies between 1 and 2 kilohertz. Individual “syllables” in the birdsong last between 10 and 300 milliseconds.

Two factors control how sounds are produced: the pressure of the air entering the syrinx from the lungs, and the elasticity of the oscillating folds. It turns out that the folds only oscillate above a certain air pressure. Previous research by physicists revealed that this motion is analogous to that of a simple nonlinear oscillator, such as a mass on a spring.

Gabriel Mindlin and Marcos Trevisan of the University of Buenos Aries in Argentina and Franz Goller at the University of Utah in the US have now taken this work one step further by considering that the two types of neural nuclei in the brain that control a bird’s breathing could also be modelled as nonlinear systems. Scientists now know that when a bird sings, an area of the its brain called the HVc is activated. This excites neurons in another area known as the RA region. Some neurons in this structure then excite motor neurons that control muscles in the vocal cords or lungs.

Coupled with experimental observations of how the pressure in the bird’s air-sac — a sac that controls the flow of air through the lungs — oscillates, the new model shows that birdsong is simply produced from the interplay between a physical substrate (the air-sac) and a neural system. “This is different to the long-held view in which a nervous system sends instructions to a ‘passive’ body,” explains Mindlin. “The result is surprising because one would think that complex behaviour, like birdsong, with its wide variety of different patterns would require a complex neural architecture,” he adds.

Mindlin believes the work could have wide-reaching implications for the animal world. “If diversity of behaviour can be understood in terms of subharmonics of nonlinear systems, many motor patterns could eventually be the result of neural architectures simpler than we think,” he states.

To confirm its model, the group is now looking for the effect in suboscines — a species of bird that has some of the same neural nuclei as canaries but lacks certain others (called telencephalics). “In this way, we would prove that the complexity does not originate at these telencephalics,” says Mindlin.


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