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The Interstellar Boundary EXplorer (IBEX) ribbon is an intense energetic neutral atom (ENA) emission feature encircling the sky, spanning energies ≤0.5–6 keV. The ribbon may be produced by the “secondary ENA” mechanism, where ENAs emitted from a source plasma population inside the heliosphere propagate outside the heliopause, undergo two charge-exchange events, and become secondary ENAs that may be directed back toward Earth and detected by IBEX. In this scenario, the source plasma population is governed by the interaction of the solar wind (SW) with the interstellar medium and is thus sensitive to the global SW properties. Moreover, this scenario predicts that the distance to the source of secondary ENAs depends on the ENA energy and SW speed, which in turn may affect the shape of the ribbon. In this paper, we use a computational model of the heliosphere with simplified SW boundary conditions to analyze the influence of ENA energy and SW speed, independent of time and latitude, on the global spatial and geometric properties of the ribbon. We find a strong dependence of the simulated ribbon energy spectrum and spatial symmetry on SW speed and ENA energy, and only a slight dependence on ribbon geometry. Our results suggest a significant number of primary ENAs from the inner heliosheath may contribute to the pickup ion source population outside the heliopause, depending on the ENA energy and SW speed. The lack of variation in the simulated ribbon center as a function of ENA energy and SW speed, in contrast to the observations, implies that the asymmetry of the SW plays an important role in determining the position of the ribbon. Comparisons to the IBEX data also signify the ribbon’s dependence on the properties of the local interstellar medium, particularly the interstellar magnetic field.