It is known that genetic polymorphisms can be maintained in populations without superiority of the heterozygote subject to constant but non-linear selection through periodic and higher-order behaviour. In this paper we explore evolutionary paths from single equilibria to higher-order attractors and the existence of polymorphisms that do not arise from equilibria. We explore whether there is a continuous range of allelic types that can create such polymorphisms. We use a single-locus genetic model with exponential density-dependent fitness functions and show that there are large parameter ranges in regions of both overdominance and partial dominance where polymorphic attractors exist.