A spin vortex consists of an in-plane curling magnetization and a small core region (~10 nm) with out-of-plane magnetization. An oscillating field or current induce gyrotropic precession of the spin vortex. Dipole-dipole and exchange coupling between the interacting vortices may lead to excitation of collective modes whose frequencies depend on the core polarities. Here we demonstrate an effective method for controlling the relative core polarities in a model system of overlapping Ni(80)Fe(20) dots. This is achieved by driving the system to a chaotic regime of continuous core reversals and subsequently relaxing the cores to steady-state motion. It is shown that any particular core polarity combination (and therefore the spectral response of the entire system) can be deterministically preselected by tuning the excitation frequency or external magnetic field. We anticipate that this work would benefit the future development of magnonic crystals, spin-torque oscillators, magnetic storage and logic elements.