  We theoretically study how the dynamics of the resistive state in narrow
superconducting channels shunted by an external resistor depends on channel's
length $L$, the applied current $j$, and parameter $u$ characterizing the
penetration depth of the electric field in the nonequilibrium superconductors.
We show that changing $u$ dramatically affects both the behaviour of the
current-voltage characteristics of the superconducting channels and the
dynamics of their order parameter. Previously, it was demonstrated that when
$u$ is less than the critical value $u_{c1}$, which does not depend on $L$, the
phase slip centers appear simultaneously at different spots of the channel.
Herewith, for $u>u_{c1}$ these centres arise consecutively at the same place.
In our work we demonstrate that there is another critical value for $u$.
Actually, if $u$ does not exceed a certain value $u_{c2}$, which depends on
$L$, the current-voltage characteristic exhibits the step-like behaviour.
However, for $u>u_{c2}$ it becomes hysteretic. In this case, with increase of
$j$ the steady state, which corresponds to the time independent distribution of
the order parameter along the channel, losses its stability at switching
current value $j_{sw}$, and time periodic oscillations of both the order
parameter and electric filed occur in the channel. As $j$ sweeps down, the
periodic dynamics ceases at certain retrapping current value $j_r<j_{sw}$.
Shunting the channel by a resistor increases the value of $j_r$, while $j_{sw}$
remains unchanged. Thus, for some high enough conductivity of the shunt $j_r$
and $j_{sw}$ eventually coincide, and the hysteretic loop disappears. We reveal
dynamical regimes involved in the hysteresis, and discuss the bifurcation
transitions between them.
