Traveling waves for a diffusive predator–prey system with general functional response

By combining the simplified shooting method with a sandwich method, the existence and nonexistence of two types of traveling wave solutions for a class of diffusive predator–prey systems with general functional response are investigated. These two types of point-to-point traveling waves include the connections of the zero equilibrium to the positive equilibrium and the boundary equilibrium to the positive equilibrium. Furthermore, we also give a discussion about the parameter threshold value whether any of the traveling waves approaches the positive equilibrium monotonically or has exponentially damped oscillations about the positive equilibrium. Some applications with different functional response functions are given to illustrate the application of our results.