  Recently, it has been shown that properties of excitable media stirred by
two-dimensional chaotic flows can be properly studied in a one-dimensional
framework \cite{excitablePRL,excitablePRE}, describing the transverse profile
of the filament-like structures observed in the system. Here, we perform a
bifurcation analysis of this one-dimensional approximation as a function of the
{\it Damk{\"o}hler} number, the ratio between the chemical and the strain
rates. Different branches of stable solutions are calculated, and a Hopf
bifurcation, leading to an oscillating filament, identified.
