  Exceptional points are found in the spectrum of a prototypical thermoacoustic
system as the parameters of the flame transfer function are varied. At these
points, two eigenvalues and the associated eigenfunctions coalesce. The
system's sensitivity to changes in the parameters becomes infinite. Two
eigenvalue branches collide at the exceptional point as the interaction index
is increased. One branch originates from a purely acoustic mode, whereas the
other branch originates from an intrinsic thermoacoustic mode. The existence of
exceptional points in thermoacoustic systems has implications for physical
understanding, computing, modeling and control.
