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.
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