Traveling wave solutions for a diffusive predator-prey model with predator saturation and competition

The purpose of this paper is to study the traveling wave solutions of a diffusive predator-prey model with predator saturation and competition functional response. The system admits three equilibria: a zero equilibrium E-0, a boundary equilibrium E-1 and a positive equilibrium E-* under some conditions. We establish the existence of two types of traveling wave solutions which connect E0 and E* and E1 and E*, respectively. Our main arguments are based on a simplified shooting method, a sandwich method and constructions of appropriate Lyapunov functions. Our particular interest is to investigate the oscillation of both types of traveling wave solutions when they approach the positive equilibrium.