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%0 Conference Proceedings
%A Vergez, Christophe
%A Rodet, Xavier
%T Bifurcation Sequence in a Physical Model of Trumpet-like Instruments : from a Fixed Point to Chaos
%D 1998
%E IEICE
%B NOLTA
%C Crans Montana
%V 2
%P 751-754
%F Vergez98a
%K Physical models
%K Bifurcation analysis
%K Trumpet
%K Hopfquasi-periodicity
%K chaos
%X 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.
%1 7
%2 3