Stability/Instability of Periodic Solutions and Chaos in Physical Models of Musical Instruments
Résumé
We study multiple solutions and chaos in simple physical models and their
stabilities. A path toward a unique solution can be based upon the low pass character of the linear element. Chaotic
signals are shown to cover a large space ranging from a sound perceived as
harmonic without noise up to an essentially noisy sound. This is a very important
feature for sound synthesis since the synthesis of noise and irregularities of
traditional instruments has always been difficult and unsatisfactory. Methods are
proposed to find the solutions and their stabilities, and to obtain controllable
systems with periodic and chaotic behaviors.
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