Nonlinear Dynamics

, Volume 74, Issue 3, pp 591–605 | Cite as

Prediction of the dynamic oscillation threshold in a clarinet model with a linearly increasing blowing pressure: influence of noise

Original Paper

Abstract

This paper presents an analysis of the effects of noise and precision on a simplified model of the clarinet driven by a variable control parameter.

When the control parameter is varied, the clarinet model undergoes a dynamic bifurcation. A consequence of this is the phenomenon of bifurcation delay: the bifurcation point is shifted from the static oscillation threshold to a higher value, called dynamic oscillation threshold.

In a previous work Bergeot et al. in Nonlinear Dyn. doi:10.1007/s11071-013-0806-y, (2013), the dynamic oscillation threshold is obtained analytically. In the present article, the sensitivity of the dynamic threshold on precision is analyzed as a stochastic variable introduced in the model. A new theoretical expression is given for the dynamic thresholds in presence of the stochastic variable, providing a fair prediction of the thresholds found in finite-precision simulations. These dynamic thresholds are found to depend on the increase rate and are independent on the initial value of the parameter, both in simulations and in theory.

Keywords

Musical acoustics Clarinet-like instruments Iterated maps Dynamic Bifurcation Bifurcation delay Transient processes Noise Finite precision 

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • B. Bergeot
    • 1
  • A. Almeida
    • 1
  • C. Vergez
    • 2
  • B. Gazengel
    • 1
  1. 1.LUNAM Université, Laboratoire d’AcoustiqueUniversité du Maine, UMR CNRS 6613Le Mans Cedex 9France
  2. 2.Laboratoire de Mécanique et Acoustique, LMACNRS UPR 7051Marseille Cedex 20France

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