In a classical slow-fast system, the phase variables can be separated into fast variables and slow variables. In singular systems, there is no such separation; only the requirement of the presence of a slow surface, i.e., a surface consisting of only singular points, at the zero value of the parameter is retained. A singular system on the plane is a one parameter family of vector fields with a curve of singular points at the zero value of the parameter. In such families, new global phenomena arise, because the phase space is no longer the Cartesian product of fast and slow variables.
The reviewed article describes one of such new global phenomena, the bifurcation of slow-fast separatrix loop. This bifurcation occurs in singular systems with additional parameters. The bifurcation diagram and phase portraits corresponding to various domains of the parameter space are constructed. The origin of the parameter plane corresponds to a singular separatrix loop, i.e., a closed curve consisting of an arc of a slow curve, one of whose endpoints is a repulsive singular point \(A\) of the slow system and the other is a jump point \(B\), and an arc of the trajectory of the fast system tangent to the slow curve at the jump point \(B\) and falling on the slow curve at the singular point \(A\). The curve \(\gamma\) in the parameter plane corresponds to a family of separatrix loops, which is called a slow-fast separatrix loop.