Dynamics of a structured population on two patches

We study a model for a creature which has a life cycle with two stages and which inhabits two patches. Our examination involves three different choices of birth function, namely linear, Ricker, and Allee. We discover conditions on the model parameters such that extinction will occur on both patches. We also find conditions on the parameters, and additionally in some cases the initial conditions, such that the creature will remain endemic on both patches. When the birth function is of Allee type on both patches, we show that there is always a population level beneath which extinction becomes inevitable on either patch. Simulations corroborate our theoretical results.