Global stability for a discrete space-time Lotka-Volterra system with feedback control (Q2205900)

Summary: 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.