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J. Bifurcation Chaos"],"published-print":{"date-parts":[[2022,2]]},"abstract":"<jats:p> In this paper, we investigate the dynamics of three-vortex systems and give a global phase diagram analysis with different types of parameters on the plane. By using the invariants to construct canonical transformations, the Hamiltonian of the three-vortex system is reduced to a desired two-dimensional Hamiltonian. Then, we analyze its phase diagrams by considering all possible situations. 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