Combined Impacts of Dispersal and Delay in a Coupled Model: Emergence of Asymmetric Steady States and Limit Cycles, Multistability Along With Population Recovery

ABSTRACT Metapopulation models are widely used in ecology to study persistence, population enhancement, and stability dynamics. In this work, we propose a two‐patch predator‐prey model coupled through delayed dispersal and uncover the emergence of dispersal‐induced coexistence states. A central objective is to discover alternative asymmetric steady states, which arise solely due to coupling and coexist with the steady states inherited from the isolated patches, apart from the inherent symmetric steady states of the isolated habitats. It is revealed that dispersal can generate multiple stable attractors, including tristability involving either three stable steady states or three stable limit cycles. Ecologically, we conclude that when the isolated habitat possesses stable coexistence, the existence of asymmetric states in the metacommunity illustrates how population abundances are catastrophically reduced or enhanced due to habitat fragmentation. We further demonstrate that dispersal delay can induce simultaneous stability switching in both symmetric and asymmetric steady states through Hopf bifurcations, producing transitions between stable steady states and cyclic mode. In another ecological application, we show that predators may go extinct in isolated patches but persist in the coupled system due to dispersal. These findings highlight the role of habitat connectivity and suggest that dispersal can promote species recovery and conservation.