Abstract
In this paper, by making use of Duan's topological current theory, the branch process of regular magnetic monopoles is discussed in detail. Regular magnetic monopoles are found generating or annihilating at the limit point and encountering, splitting, or merging at the bifurcation point and the degenerate point systematically of the vector order parameter field ϕ⃗(x). Furthermore, it is also shown that when regular magnetic monopoles split or merge at the degenerate point of field function ϕ⃗, the total topological charges of the regular magnetic monopoles are still unchanged.
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