Summary
We investigate the multistable dynamics of a simple model of reed musical instrument written as a system of four ordinary differential equations. A bifurcation analysis is performed considering the blowing pressure – which is the main control parameter for the musician – as a bifurcation parameter. This unveils that several stable periodic solutions corresponding to different musical notes coexist on a range of the blowing pressure. We employ a machine learning technique (namely an explicit design space decomposition technique combined with an support-vector learning machine) to construct, in an well-chosen 3D subspace of the phase space, the boundary between the basins of attraction of the coexisting periodic solutions. Basins are of particular interest from a practical point of view: they relate to the playability of the regimes and to their sensitivity to perturbations.
