Global Structure of Bifurcating Solutions of Some Reaction-Diffusion Systems

We study the global structure of the set of bifurcating solutions of a class of coupled nonlinear reaction-diffusion systems. Our main result is that when one of the diffusion coefficients is sufficiently large, the bifurcating branch emanating from a uniform state continues to exist until it is connected to the singularly perturbed solutions which contain interior transition layers (Theorem 6.1). We also present a global branching theorem for the bifurcating branch which shows that in the general situation it does not fall entirely on the trivial branch (Theorem 2.2).