Diffusion has no influence on the global asymptotical stability of the Lotka–Volterra prey–predator model incorporating a constant number of prey refuges

摘要

By constructing a suitable Lyapunov function, we obtain the global asymptotical stability of the Lotka–Volterra prey–predator model incorporating a constant number of prey refuges and diffusion. It is shown that diffusion has no influence on the global asymptotical stability of the system with homogeneous Neumann boundary condition.