Prediction of the dynamic oscillation threshold in a clarinet model with a linearly increasing blowing pressure: influence of noise
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- Bergeot, B., Almeida, A., Vergez, C. et al. Nonlinear Dyn (2013) 74: 591. doi:10.1007/s11071-013-0991-8
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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.