  Motivated by a stochastic differential equation describing the dynamics of
interfaces, we study the bifurcation behavior of a more general class of such
equations. These equations are characterized by a 2-dimensional phase space
(describing the position of the interface and an internal degree of freedom).
The noise accounts for thermal fluctuations of such systems. The models
considered show a saddle-node bifurcation and have furthermore homoclinic
orbits, i.e., orbits leaving an unstable fixed point and returning to it. Such
systems display intermittent behavior. The presence of noise combined with the
topology of the phase space leads to unexpected behavior as a function of the
bifurcation parameter, i.e., of the driving force of the system. We explain
this behavior using saddle point methods and considering global topological
aspects of the problem. This then explains the non-monotonous force-velocity
dependence of certain driven interfaces.
