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Dyon solutions with axial symmetry in Yang–Mills–Higgs theory, including monopole–antimonopole pairs (MAP), monopole–antimonopole chains (MAC) and vortex-rings are introduced previously. The previously studied cases include at most a bifurcation for MAP systems and two for MAC dyon solutions. Here, for the case of [Formula: see text]-winding number [Formula: see text], a rich set of solutions including nine branches and four bifurcations, has been obtained for electrically charged four-pole MAC solutions. Also, the transition between two different charge configurations at a lower energy bifurcating branch is detected for the first time. This study also improves and completes some aspects of a previous study on the electrically neutral case. In the case of [Formula: see text], in addition to previously found bifurcation, another bifurcation at small values of Higgs self-coupling constant [Formula: see text], has been obtained here.

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