Abstract
In this paper, we propose and study a fractional Caputo-difference map based on the 2D generalized Hénon map. By means of numerical methods, we use phase plots and bifurcation diagrams to investigate the rich dynamics of the proposed map. A 1D synchronization controller is proposed similar to that of Pecora and Carrol, whereby we assume knowledge of one of the two states at the slave and replicate the second state. The stability theory of fractional discrete systems is used to guarantee the asymptotic convergence of the proposed controller and numerical simulations are employed to confirm the findings.