  We investigate the non-linear dynamics of a two-dimensional film flowing down
a finite heater, for a non-volatile and a volatile liquid. An oscillatory
instability is predicted beyond a critical value of Marangoni number using
linear stability theory. Continuation along the Marangoni number using
non-linear evolution equation is used to trace bifurcation diagram associated
with the oscillatory instability. Hysteresis, a characteristic attribute of a
sub-critical Hopf bifurcation, is observed in a critical parametric region. The
bifurcation is universally observed for both, a non-volatile film and a
volatile film.
