Global stability for a semidiscrete logistic system with feedback control (Q2194590)

Summary: In this paper, a semidiscrete logistic model with the Dirichlet boundary conditions and feedback controls is proposed. By means of the sub- and supper-solution method and eigenvalue theory, the unique positive equilibrium is proved. By constructing a suitable Lyapunov function, the global asymptomatic stability of the unique positive equilibrium is investigated. Finally, numerical simulations are presented to verify the effectiveness of the main results.