Stability and bifurcation in a reaction–diffusion model with nonlinear boundary conditions

Abstract

In this paper, we investigate the existence, stability, local and global bifurcation of the steady state solutions for a diffusive logistic model with nonlinear boundary conditions. Supercritical and subcritical bifurcation of steady state solutions are obtained by virtue of the Crandall–Rabinowitz theorem and the Lyapunov–Schmidt reduction. The local stability and the possibility of obtaining an Allee effect are also analyzed. Furthermore, the result on global bifurcation is obtained as well by employing the Rabinowitz theorem.