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By making use of ϕ-mapping topological current theory and the decomposition of gauge potential theory, we investigate the skyrmion excitations of spin Hall effect induced by optical fields in neutral atomic system. It is shown that the topological structures of these skyrmions are characterized by ϕ-mapping topological numbers: Hopf indices and Brouwer degrees. Based on the bifurcation theory of ϕ-mapping theory, it is found that the skyrmions can be generated or annihilated at the limit point and they encounter, split or merge at the bifurcation point.