Analysis on existence of bifurcation solutions for a predator-prey model with herd behavior

This paper is concerned with a diffusive predator-prey model with herd behavior. The local and global stability of the unique homogeneous positive steady state U* is obtained. Treating the conversion or consumption rate γ as the bifurcation parameter, the steady-state bifurcations both from simple and double eigenvalues are studied near U*. The techniques include the Lyapunov function, the spectrum analysis of operators, the bifurcation theory, space decompositions and the implicit function theorem.