Stability and bifurcation in a single species with nonlinear boundary conditions

Abstract

A single-species model subject to nonlinear boundary conditions is investigated. Existence, nonexistence, and local/global asymptotical stability of positive steady-state solutions are shown to identify the ranges of parameters, the growth rate functions, and boundary reaction functions. In particular, we show that the model can have multiple equilibria and in some parameter ranges can support Allee effects.