Abstract
The purpose of this paper is to study the effect of diffusion in the existence of non-constant steady states for the Lotka–Volterra competition-diffusion system with three species, under Neumann boundary conditions. It will be shown that two large diffusion rates prevent the appearance of non-constant steady states, while if just one species diffuses fast non-constant equilibria may arise. The existence is shown by two methods, degree theory and bifurcation techniques. The stability of bifurcating steady states will be established.
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