Boundedness and permanence in a class of periodic time-dependent predator–prey system with prey dispersal and predator density-independence

In this paper, we study two species predator–prey Lotka–Volterra type dispersal system with periodic coefficients, in which the prey species can disperse among n patches, while the density-independent predator species is confined to one of the patches and cannot disperse. Sufficient conditions on the boundedness, permanence and existence of positive periodic solution for this system are established. The theoretical results are confirmed by a special example and numerical simulations.