New Results on Shape Synchronization in the Drive-Response Scheme of a Class of 2D Fractional-Order Discrete-Time Chaotic Systems

Year 2025, Volume: 7 Issue: 3, 186 - 196

Hamid Hamiche , Ouerdia Megherbi , Karim Kemih , Mourad Laghrouche

https://doi.org/10.51537/chaos.1650994

Abstract

In this article, we investigate shape synchronization within the drive-response framework for a specific class of 2D discrete-time noninteger-order chaotic dynamics. To achieve synchronization between the driver and response systems, we formulate a novel theorem that establishes a specific control law. This control strategy is meticulously developed to synchronize the chaotic attractors's shapes in the driver-response scheme. A rigorous proof of the theorem is provided, demonstrating its theoretical soundness. The effectiveness of the synchronization technique is validated through extensive numerical simulations. The results show that the synchronization error converges asymptotically to zero, with fast convergence speed, confirming the reliability of the control scheme. Moreover, the response system successfully replicates the geometric structure of the drive system's attractor, demonstrating precise shape synchronization. Using a discrete-time fractional-order chaotic system offers significant advantages, including increased dynamical complexity and a broader key space, which enhance the system's potential for secure communication and encryption applications. Furthermore, shape synchronization allows for the preservation of topological features in chaotic signals, making it particularly useful in applications where structural integrity of the transmitted chaotic signal is essential.

Keywords

2D chaotic systems , Discrete-time systems , Asymptotic shape synchronization , Fractional-order systems

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