Traveling Wave Solution in a Diffusive Predator-Prey System with Holling Type-IV Functional Response

Abstract

We establish the existence of traveling wave solution for a reaction-diffusion predator-prey system with Holling type-IV functional response. For simplicity, only one space dimension will be involved, the traveling solution equivalent to the heteroclinic orbits in $R^{\mathrm{3}}$. The methods used to prove the result are the shooting argument and the invariant manifold theory.