Synchronizing Newton-Leipnik Fractional Order Chaotic Systems by Sliding Mode Control and Applying in Secure Color Image Communication

In this paper, we present a comprehensive investigation of a sliding mode control (SMC) method, with a focus on its application to synchronize a three-dimensional (3-D) chaotic Newton-Leipnik system with fractional order. This study aims to demonstrate the robustness and efficiency of the SMC technique in addressing the challenges of synchronization in chaotic systems. The proposed control method is rigorously analyzed using Lyapunov stability theory, ensuring that the system’s behavior converges smoothly towards synchronization. The reliability of this approach is validated through both theoretical and practical evaluations.To further assess the performance of the sliding mode control method, MATLAB simulations were conducted, comparing the SMC technique to a conventional PID controller as well as other advanced methods in the context of secure color image communication. The results showed that SMC outperformed these techniques, achieving a lower Root Mean Square Error (RMSE) and a higher Signal-to-Noise Ratio (SNR), which are key indicators of communication security and effectiveness. Additionally, static analyses such as histogram, Mean Square Error (MSE), and SNR measurements highlighted the system's enhanced security and potential for robust image communication applications. These findings emphasize the practical significance of SMC in secure and reliable communication systems.