Persistence and global stability of positive periodic solutions of three species food chains with omnivory

In this paper, we investigate the existence and global stability of the positive periodic solutions of delayed discrete food chains with omnivory. With the help of continuation theorem in coincidence degree theory and Lyapunov functions, some sufficient conditions are obtained. The results show that, for such a system with omnivory, more conditions are required for the persistence of the positive periodic solutions than that of a linear food chain. On the other hand, omnivory makes no differences on the stability of the solutions.