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J. Bifurcation Chaos"],"published-print":{"date-parts":[[2022,6,30]]},"abstract":"<jats:p> In this paper, we study the global dynamics of continuous piecewise quadratic Hamiltonian systems separated by the straight line [Formula: see text], where these kinds of systems have a nilpotent center at [Formula: see text], which comes from the combination of two cusps of both Hamiltonian systems. By the Poincar\u00e9 compactification we classify the global phase portraits of these systems. 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