Bifurcation analysis of a two-species diffusive model

Abstract This paper is devoted to studying a two species model with reaction–diffusion term under the robin boundary condition. By applying Lyapunov–Schmidt reduction, implicit function theorem, bifurcation theory, the principal spectral theory and other important formulas, we obtain the existence and stability of the spatial nonhomogeneous steady state solutions bifurcating from a double eigenvalue under some given parameters conditions.