Almost periodic solution of non-autonomous Lotka–Volterra predator–prey dispersal system with delays

This paper studies a non-autonomous Lotka–Volterra almost periodic predator–prey dispersal system with discrete and continuous time delays which consists of n-patches, the prey species can disperse among n-patches, but the predator species is confined to one patch and cannot disperse. By using comparison theorem and delay differential equation basic theory, we prove the system is uniformly persistent under some appropriate conditions. Further, by constructing suitable Lyapunov functional, we show that the system is globally asymptotically stable under some appropriate conditions. By using almost periodic functional hull theory, we show that the almost periodic system has a unique globally asymptotical stable strictly positive almost periodic solution. The conditions for the permanence, global stability of system and the existence, uniqueness of positive almost periodic solution depend on delays, so, time delays are “profitless”. Finally, conclusions and two particular cases are given. These results are basically an extension of the known results for non-autonomous Lotka–Volterra systems.