The Dynamics and Control of the Fractional Forms of Some Rational Chaotic Maps

This paper proposes three fractional discrete chaotic systems based on the Rulkov, Chang,and Zeraoulia–Sprott rational maps. The dynamics of the proposed maps are investigated by means of phase plots and bifurcations diagrams. Adaptive stabilization schemes are proposed for each of the three maps and the convergence of the states is established by using the Lyapunov method. Furthermore, a combination synchronization scheme is proposed whereby a combination of the fractional Rulkov and Chang maps is synchronized to the fractional Zeraoulia-Sprott map. Numerical results are used to confirm the findings of the paper.