Numerical simulation and qualitative analysis for a predator–prey model with B–D functional response

We consider a predator–prey model with Beddington–DeAngelis functional response subject to the homogeneous Neumann boundary condition. We study the local and global stability of the unique positive constant solution, the nonexistence of nonconstant positive solution. By bifurcation theorem we obtain one sufficient condition of the existence of nonconstant positive steady state solution in one dimensional case. Furthermore, in numerical simulation, we design a path to analyze and complement our theoretical results.