Steady-state dynamics in a two-patch population model with and without Allee effect (Q6575025)

In this paper, the authors consider the evolution of a biological population in a heterogeneous environment consisting of two adjacent patches of different quality, leading to a system of reaction-diffusion equations ``glued'' at the interface, with no-flux boundary conditions and general growth functions that account for the occurrence of Allee effects.\N\NOf concern are the existence, stability and bifurcation of steady states. For the former, the corresponding eigenvalue problem is analyzed, leading to a generalization of Sturm-Liouville theory to the available settings, while the latter is discussed via a combination of linear analysis, sub- and supersolution methods and bifurcation results. Notably, the occurrence of a fold bifurcation, commonly associated with strong Allee effects, is observed. Finally, the previously obtained theoretical results are used to discuss an approach towards species conservation via varying the patch size.