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Many populations of animals or plants, exhibit a metapopulation structurewith close, spatially-separated subpopulations. The field of metapopulationtheory has made significant advancements since the influential Levins model.Various modeling approaches have provided valuable insights to theoreticalEcology. Despite extensive research on metapopulation models, there are stillchallenging questions that are difficult to answer from ecologicalmetapopulational data or multi-patch models. Low-dimension mathematical modelsoffer a promising avenue to address these questions, especially for globaldynamics which have been scarcely investigated. In this study, we investigate atwo-patch metapopulation model with logistic growth and diffusion betweenpatches. By using analytical and numerical methods, we thoroughly analyze theimpact of diffusion on the dynamics of the metapopulation. We identify theequilibrium points and assess their local and global stability. Furthermore, weanalytically derive the optimal diffusion rate that leads to the highestmetapopulation values. Our findings demonstrate that increased diffusion playsa crucial role in the preservation of both subpopulations and the fullmetapopulation, especially under the presence of stochastic perturbations.Specifically, at low diffusion values, the origin is a repeller, causing orbitsstarting around it to travel closely parallel to the axes. This configurationmakes the metapopulation less resilient and thus more susceptible to local andglobal extinctions. However, as diffusion increases, the repeller transitionsto a saddle point, and orbits starting near the origin rapidly converge to theunstable manifold of the saddle. This phenomenon reduces the likelihood ofstochastic extinctions and the metapopulation becomes more resilient due tothese changes in the vector field of the phase space.

Dispersal-enhanced resilience in two-patch metapopulations: origin's instability type matters