Existence of periodic solutions in a nonautonomous food web with Beddington–DeAngelis functional response

In this paper, we investigate the existence of positive T-periodic solutions in a food web with one predator feeding on n preys by Leray–Schauder degree theory, which plays a significant role on further studying the uniqueness of limit cycles of this food web model. We start with a series of required spaces and operators and construct a bounded open set Ω over which the corresponding Leray–Schauder degree can be well-defined. Afterwards, by the invariance property of homotopy, we verify that the Leray–Schauder degree is not equal to 0 under certain conditions, thus implying the existence of positive T-periodic solutions. Finally, a numerical example is presented to illustrate our result.