Global Stability for a Discrete Space-Time Lotka–Volterra System with Feedback Control

الملخص EN

In this paper, a discrete space-time Lotka–Volterra model with the periodic boundary conditions and feedback control is proposed.

By means of a discrete version of comparison theorem, the boundedness of the nonnegative solution of the system is proved.

By the combination of the Volterra-type and quadratic Lyapunov functions, the global asymptomatic stability of the unique positive equilibrium is investigated.

Finally, numerical simulations are presented to verify the effectiveness of the main results.