Abstract

The aim of this work is to investigate the existence and non-existence of traveling wave solutions for a diffusive three species model involving omnivory. The minimal speed c∗of traveling wave solutions of the model is charaterized. If the wave speed is greater than or equal to c∗, we show the existence of traveling wave solutions con- necting trivial and positive equilibria by combining the upper and lower solutions with the contracting rectangle. On the other hand, if the wave speed is less than c∗, the non-existence of such solutions is also established. Finally, to illustrate our theoretical results, some numerical simulations are performed and biological meanings are interpreted.