  We study thermal instability in NbN superconducting stripline resonators. The
system exhibits extreme nonlinearity near a bifurcation, which separates a
monostable zone and an astable one. The lifetime of the metastable state, which
is locally stable in the monostable zone, is measure near the bifurcation and
the results are compared with a theory. Near bifurcation, where the lifetime
becomes relatively short, the system exhibits strong amplification of a weak
input modulation signal. We find that the frequency bandwidth of this
amplification mechanism is limited by the rate of thermal relaxation. When the
frequency of the input modulation signal becomes comparable or larger than this
rate the response of the system exhibits sub-harmonics of various orders.
