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 (EPs) are found in the spectrum of a longitudinal thermoacoustic system
as the parameters of the flame transfer function are varied. EPs occur when two eigenvalue
trajectories with different physical nature collide: One trajectory originates from an acoustic
mode, whereas the other trajectory originates from an intrinsic thermoacoustic mode. The
system's sensitivity to changes in the parameters is infinite because the EP is a square-root
branch point of the determinant. Traditional iterative methods to find eigenvalues are not …