Analysis on existence of bifurcation solutions for a predator prey model with herd behavior
Abstract 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 g 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.