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Bifurcation Sequence in a Physical Model of Trumpet-like Instruments : From a Fixed Point to Chaos

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text
 

Genre(s)

article
 

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document imprimé
 

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Titre

Bifurcation Sequence in a Physical Model of Trumpet-like Instruments
 

Sous-Titre

From a Fixed Point to Chaos
 

Nom(s)

Vergez, Christophe (auteur)
 
Rodet, Xavier (auteur)
 

Publication

Crans Montana, Suisse , Presses Polytechniques et Universitaires Romandes, 1998
 

Description

Sujet(s)

Physical models   Bifurcation analysis   Trumpet   Hopfquasi-periodicity   chaos
 

Résumé

We have built a numerical model of trumpet-like instruments. Since the understanding of the model's behavior is desirable for a musical usage, we have studied the model in the framework of the theory of the nonlinear dynamical systems. The blowing pressure has been chosen as the bifurcation parameter. We have been able to predict, according to the frequential version of the Hopf theorem, the critical threshold at which a stable fixed point looses its stability and gives birth to a unique stable limit cycle. Moreover, amplitude and frequency of the limit cycle have been forecasted to an excellent approximation. By still increasing the blowing pressure, a secondary supercritical Hopf bifurcation has been obtained, leading to a quasi-periodic motion on a two-torus. Finally, with a further increase in blowing pressure, the progressive destruction of the two-torus has been observed, leading to a chaotic motion.
 

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Contribution au colloque ou congrès : NOLTA
 

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Date de la notice

2006-03-14 01:00:00
 

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