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tokens: shifts of the energy-release region along the separator. Nevertheless, some hints concerning this issue can be drawn from the behavior of the emission spots as function of the radii of the energy-release spheres R , which are plotted by various colors in Figs. 3 and 5 . We also checked the patterns of emission obtained under the similar assumptions in a few other topological models of solar magnetic fields (i.e., involving the bifurcations of null points). In these models, however, we did not find the behavior of the ribbons as rich as in the GKSS model. This is most probably because only the latter model exhibits the genuine topological instability, i.e., when a small rearrangement of the magnetic sources results in the dramatic reconstruction of the magnetic field lines in the entire space. In summary, the four-ribbon configurations exist only in a quite small semilunar region of topological instability (where the bifurcation takes place); at all other locations of the fourth magnetic source, a three- (or even two-)ribbon emission appears. Hence, we should expect that fraction of the four-ribbon flares will be sufficiently small because of the relatively small area of the region of topological instability. This prediction agrees very well with the observations. Most of the anemone flares detected by Hinode satellite possess three ribbons; the four-ribbon flares also exist but they are formed seldomly. This is why we believe that our topological model, although not universal, provides a reasonable interpretation of the relevant phenomena by varying only a single parameter. Appendix A: Basic parameters of the separator in the two-dome structure In general, computing a spatial configuration of the separator is a non-trivial task: the separator is an inherently unstable structure, since any field line originating in its neighborhood quickly deviates outward. So, the straightforward numerical integration is meaningless, and a more elaborate type of algorithm should be applied. In the present work, we used the following procedure: Since footpoints of the separator, ( x f1 , y f1 ) and ( x f2 , y f2 ), are actually the null points of the magnetic field in z = 0 plane, we calculated the distribution of B 2 in this plane, sought for its minima, and finally checked that B 2 = 0 in these minima (and, therefore, B = 0). The analysis of the scalar function B 2 ( x , y ) was employed only because, from the computational point of view, it is much more simple and robust than the analysis of the vector field B ( x , y ). To find a position of the separator above the plane z = 0, we analyzed the following “global” behavior of the magnetic field lines: (a) First of all, we fixed a vertical plane intersecting the line connecting the opposite footpoints of the separator ( x f1 , y f1 , 0) and ( x f2 , y f2 , 0); to get a better accuracy, it is desirable that this plane be approximately perpendicular to the line. (b) Then, we generated a mesh of points