Uniqueness of periodic solutions of a nonautonomous density-dependent predator-prey system

In this present paper, we investigate the uniqueness of periodic solutions of a nonautonomous density-dependent and ratio-dependent predator-prey system, where not only the prey density dependence but also the predator density dependence are considered, such that the studied predator-prey system conforms to the realistically biological environment. We start with a sufficient condition for the permanence of the system and then construct a weaker sufficient condition by introducing a specific set, denoted as Γ. Based on this Γ and the Brouwer fixed-point theorem, we obtain the existence condition of positive periodic solutions. Moreover, since the uniqueness of positive periodic solutions can be ensured by global attractiveness, we alternatively introduce a sufficient condition for global attractiveness. Similarly, we also provide a sufficient condition for the uniqueness of non-negative periodic solutions.