Steady state bifurcation in a cross-diffusion prey-predator model

In this paper, we study the bifurcation of nontrivial steady state solutions for a cross-diffusion prey-predator model with homogeneous Neumann boundary conditions. The existence of positive steady state solutions near a bifurcation point is proved using a crossing curve bifurcation theorem. We consider a situation where the transversality condition is not satisfied. Unlike the case in saddle-node bifurcation, the solution set is a pair of transversally intersecting curves.