Multiple cyclic sets connecting saddle points and limit cycles of a four-species system and its uniform persistence

Considering a model of a generalized Gause-type four-species system of two predator-prey pairs linked by competition, the authors derive sufficient conditions for the existence of three different invariant cyclic sets connecting saddle points and limit cycle(s) on the boundary of its state space. Also discussed is the uniform persistence of the model in the presence of such cycle sets.