In the paper, a planar relativistic self-dual Chern-Simons model, with two Higgs particles and two gauge fields is considered. The main purpose is to locate all the possible values of the magnetic fluxes for the radially symmetric non-topological solitons. As has been known, the non-topological fluxes are not quantized. We further show that the value set of the non-topological fluxes exactly form a planar continuum portrayed by a certain hyperbolic region.
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