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The classification, up to a center-affinity, of the homogeneous quadraticdifferential systems defined on $\mathbb{R}^{3}$ that have at least asemisimple nonsingular derivation, is achieved. It is proved that there existfour affine-equivalence classes of such systems, only.

Quadratic Differential Systems on $\mathbb{R}^{3}$ Having a Semisimple Derivation