Summary
In this communication, we investigate the dynamics of a simple model of reed musical instrument with a time-varying blowing pressure accounting for attack transients performed by the musician. Indeed, when playing a reed instrument (such as the clarinet), initial acoustical transients (i.e., beginning of a note) are of critical importance. In practice, we study a toy model written as a one-dimensional non-autonomous dynamical system obtained by slowly varying in time a bifurcation parameter of the corresponding autonomous model with constant bifurcation parameter. The study focuses on the case where the time-varying parameter crosses the bistability region of the autonomous system. In the framework of the geometric singular perturbation theory (GSPT), we show that a single solution of the system can be used to describe its the global behavior. This allows to predict, depending on initial conditions and rate of change of the blowing pressure, whether or not a sound is produced during transient.
