Existence of traveling wave solutions for Gause-type models of predator-prey systems

This paper deals with the existence of three types of traveling waves for a general predator-prey systems of Gause type: traveling wave train solution, point-to-point and point-to-periodic traveling wave solutions. Applying the methods of Wazewski theorem, LaSalle's invariance principle and Hopf bifurcation theorem, we obtain the existence results. Also, the minimal wave speed for biological invasion is obtained. Furthermore, some applications are given to illustrate our results.