In this paper, a nonautonomous predator-prey model with diffusion and continuous time delay is studied, where all parameters are time-dependent. The system, which is composed of two Lotka-Volterra patches, has two species: one can diffuse between two patches, but the other is confined to one patch and cannot diffuse. It is proved that the system is uniformly persistent under appropriate conditions. Furthermore, sufficient conditions are established for global stability of the system.
Song, X., & Chen, L. (1998). Persistence and global stability for nonautonomous predator-prey system with diffusion and time delay. Computers and Mathematics with Applications, 35(6), 33–40. https://doi.org/10.1016/S0898-1221(98)00015-7