A delayed impulsive food chain system with prey refuge and mutual inference of predator

Abstract In this paper, a three-species delayed food chain system with mutual interference and impulses is established. By utilizing the continuation theorem, the comparison theorem, some analysis techniques, and constructing a suitable Lyapunov functional, some sufficient conditions for the existence of positive periodic solutions, permanence, and global attractivity of the system are obtained. The conditions obtained are related to the mutual interference constant m, prey refuge constant θ, delays, and impulses. An example is given to show the feasibility of the results.