Competitive localization

Many problems may be cast into the form of entities utilizing resources and competing for those resources. Several models inspired by such competition have previously been shown to exhibit clumping and in some cases localization in their stable equilibrium states. We show that such localization, which we wish to call ‘competitive localization’, is generic, and we provide techniques to accurately find the equilibrium states when competitive localization occurs. We also expose some difficulties in relying on numerical simulations when exploring models of this type.