A model for the diffusion of populations in annular patchy environments
A system of reaction-diffusion differential equations is utilized to model the diffusion of a population through annular patches with different carrying capacities. In the case of continuous solutions with continuous flux, it is shown that a unique, positive steady-state solution exists. In the case of radially symmetric initial conditions, it is shown that all solutions of the Cauchy problem approach this steady-state solution. Models involving nonsymmetric initial conditions are also considered.