Novel Control Law for the Fractional-order Chaotic Duffing Map

The work reported in this paper concerns a study of chaos control of fractional-order maps, especially the two-dimensional fractional-order Duffing map, which is outlined here in the sense of the Caputo h-difference operator. For the purpose of stabilizing the dynamics of the established map, some simple linear control laws are proposed and verified numerically. The chaos control is accomplished by introducing a novel result which its proof relies on selecting a suitable Lyapunov function and proper linear control law. Several numerical simulations are performed to emphasize the influence of the established scheme.