Global Stability for a Semidiscrete Logistic System with Feedback Control

Abstract EN

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.