Source-tract coupling in birdsong production

EZEQUIEL M. ARNEODO; GABRIEL B. MINDLIN

PHYSICAL REVIEW E - STATISTICAL PHYSICS, PLASMAS, FLUIDS AND RELATED INTERDISCIPLINARY TOPICS

American Physical Society

Año: 2009 vol. 79 p. 619211 - 619217

1063-651X

Birdsong is a complex phenomenon, generated by a nonlinear vocal devicecapable of displaying complex solutions even under simplephysiological motor commands. Among the peripheral physical mechanismsresponsible for the generation of complex sounds in songbirds, theunderstanding of the dynamics emerging from the interaction betweenthe sound source and the upper vocal tract remains most elusive. Inthis work we study a highly dissipative limit of a simple sound sourcemodel interacting with a tract, mathematically described in terms of a delay differential equation. We explore the system numerically and, by means of reducing the problem to a phase equation, we are capable of studying its periodic solutions.Close in parameter space to the point where the resonances of thetract match the frequencies of the uncoupled source solutions, we findcoexistence of periodic limit cycles. This hysteresis phenomenonallows us to interpret recently reported features found in thevocalization of some songbirds, in particular, ``frequency jumps´´.