N. H. Fletcher and T. D. Rossing, The Physics of Musical Instruments, 1991.

J. Kergomard and A. Chaigne, Acoustique des instruments de musique, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00455011

W. E. Worman, Self-sustained nonlinear oscillations of medium amplitude in clarinet-like systems, 1971.

N. Grand, J. Gilbert, and F. Laloë, Oscillation threshold of woodwind instruments, Acustica -Acta Acustica, pp.137-151, 1996.

A. I. Mees and L. O. Chua, The Hopf bifurcation theorem and its applications to nonlinear oscillations in circuits and systems, IEEE transactions on circuits and systems CAS-26, pp.235-254, 1979.
DOI : 10.1109/TCS.1979.1084636

D. J. Allwright, Harmonic balance and the Hopf bifurcation, Math. Proc. Camb, pp.82-453, 1977.
DOI : 10.1007/BF00248886

A. I. Mees, Describing Functions: Ten Years On, IMA Journal of Applied Mathematics, vol.32, issue.1-3, pp.221-233, 1984.
DOI : 10.1093/imamat/32.1-3.221

M. Haragus and G. Iooss, Local methods in infinite dimensional dynamical systems, EDP Sciences, 2009.

G. Dangelmayr, B. Fiedler, K. Kirchgässner, and A. Mielke, Dynamics of nonlinear waves in dissipative systems, Pitman research notes in mathematics, series 352, 1996.

M. G. Crandall and P. H. Rabinowitz, The Hopf Bifurcation Theorem in infinite dimensions, Archive for Rational Mechanics and Analysis, vol.41, issue.1, pp.53-72, 1978.
DOI : 10.1007/BF00280827

F. Gazzola and M. Squassina, Global solutions and finite time blow up for damped semilinear wave equations??????The first author was partially supported by the Italian MIUR Project ???Calcolo delle Variazioni??? while the second author was partially supported by the Italian MIUR Project ???Metodi Variazionali e Topologici nello Studio dei Fenomeni Nonlineari??? and by the INdAM., Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.23, issue.2, pp.185-207, 2006.
DOI : 10.1016/j.anihpc.2005.02.007

I. Chueshov, I. Lasiecka, and D. Toundykov, Global Attractor for a Wave Equation with Nonlinear Localized Boundary Damping and a Source Term of Critical Exponent, Journal of Dynamics and Differential Equations, vol.39, issue.2, pp.269-314, 2009.
DOI : 10.1007/s10884-009-9132-y

J. M. Coron, Periodic solutions of a nonlinear wave equation without assumption of monotonicity, Mathematische Annalen, vol.290, issue.2, pp.273-285, 1983.
DOI : 10.1007/BF01455317

F. Silva, J. Kergomard, C. Vergez, and J. Gilbert, Interaction of reed and acoustic resonator in clarinetlike systems, The Journal of the Acoustical Society of America, vol.124, issue.5, pp.3284-3295, 2008.
DOI : 10.1121/1.2988280

URL : https://hal.archives-ouvertes.fr/hal-00197147

B. Ricaud, P. Guillemain, J. Kergomard, F. Silva, and C. Vergez, Behavior of reed woodwind instruments around the oscillation threshold, accepted for publication in Acta Acustica -Acustica, 2009.

J. Gilbert, J. Kergomard, and E. Ngoya, Calculation of the steady???state oscillations of a clarinet using the harmonic balance technique, The Journal of the Acoustical Society of America, vol.86, issue.1, pp.35-41, 1989.
DOI : 10.1121/1.398352

URL : https://hal.archives-ouvertes.fr/hal-00924465

B. Cochelin and C. Vergez, A high order purely frequency-based harmonic balance formulation for continuation of periodic solutions, Journal of Sound and Vibration, vol.324, issue.1-2, pp.1-2, 2009.
DOI : 10.1016/j.jsv.2009.01.054

URL : https://hal.archives-ouvertes.fr/hal-00315288

J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, 1983.

M. Reed and B. Simon, Methods of modern mathematical physics. II: Fourier analysis, self adjointness , Academic press, 1975.

J. Kergomard, S. Ollivier, and J. Gilbert, Calculation of the Spectrum of Self-Sustained Oscillators Using a Variable Truncation Method: Application to Cylindrical Reed Instruments, Acta Acustica, vol.86, pp.685-703, 2000.