A singular perturbation result in competition theory

This paper establishes a generalized version of the singular perturbation results given by V. Hutson et al. [10, Theorem 4.1] and X. He and W.M. Ni [6, Theorem 4.2 (iii)]. In particular, it ascertains the limiting profiles of the coexistence states of the classical Lotka–Volterra model for two competing species as the diffusion coefficients approximate zero. They are provided by the global attractors of the underlying non-spatial model whenever they exist.