This paper investigates the existence of traveling wave solution to a three species reaction-diffusion system with delays, which includes competitive relationship, cooperative relationship and predator-prey relationship. By using the method of upper-lower solutions, the cross iteration method and Schauder's fixed point theorem, the existence of a traveling wave solution is obtained. MSC: 92D25; 35K57

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In this paper, we consider a discrete predator-prey system with feedback and time delays. By applying the theory of difference inequality, as well as analysis technique, sufficient conditions are obtained for the permanence of the system. And by applying Mawhin's coincidence degree theory, we obtain the existence of the positive periodic solutions.