Can a bifurcation diagram contain loops?

The bifurcation diagram plays a major role in the study of the phase topology of completely Liouville-integrable Hamiltonian systems. In the works of A.T. Fomenko and A.V. Bolsinov, the problem of the permissible form of bifurcation diagrams is formulated. In particular, can a bifurcation diagram contain loops? The answer is positive. In this paper, the critical set of the integral mapping and the bifurcation diagram, which contains or almost contains a loop, is given by the example of the vortex dynamics problem.