Abstract
This paper presents a chaotic map's fractionalization, dynamical analysis, control, and synchronization in a leader-follower configuration. The fractional-order version of the chaotic map is obtained based on the Caputo-like delta difference operator. Then, the dynamical behaviors associated with the fractional-order difference system are analyzed by employing the phase portraits, bifurcations diagrams, and Lyapunov exponent. Afterward, the control and synchronization are achieved by proposing a controller for the fractional-order map. Finally, the synchronization error based on the proposed control scheme is proven, and numerical simulations confirm that the control technique can quickly stabilize and synchronize the fractional-order chaotic maps.
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