On stabilization, synchronization and dynamical analysis of a fractional-order chaotic map

https://doi.org/10.58571/CNCA.AMCA.2022.086

Resumen: 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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E. Zambrano-Serrano, C. Posadas-Castillo, M. A. Platas-Garza, J. Rodriguez-Maldonado & A. E. Loya-Cabrera. On stabilization, synchronization and dynamical analysis of a fractional-order chaotic map. Memorias del Congreso Nacional de Control Automático, pp. 504-509, 2022. https://doi.org/10.58571/CNCA.AMCA.2022.086

Palabras clave

Sistemas Caóticos; Control de Sistemas No Lineales; Sincronización de Sistemas

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