  The current-voltage characteristics of long and narrow superconducting
channels are investigated using the time-dependent Ginzburg-Landau equations
for complex order parameter. We found out that the steps in the current voltage
characteristic can be associated with bifurcations of either steady or
oscillatory solution. We revealed typical instabilities which induced the
singularities in current-voltage characteristics, and analytically estimated
period of oscillations and average voltage in the vicinity of the critical
currents. Our results show that these bifurcations can substantially complicate
dynamics of the order parameter and eventually lead to appearance of such
phenomena as multistability and chaos. The discussed bifurcation phenomena
sheds a light on some recent experimental findings.
