Fractional-Order Dynamics and Sliding Mode Synchronization of Shimizu-Morioka System and its Application to Audio Transmission

Abstract This paper aims to study novel dynamics of the fractional-order Shimizu-Morioka system and achieve synchronization using a sliding model synchronization scheme. The complex dynamics of this system are investigated through bifurcation analysis, Lyapunov exponent computation, and complexity measures such as spectral entropy. These analysis reveal how the fractional order alters the system attractors, bifurcation structures, and chaotic behavior. Subsequently, the core problem of synchronization is addressed. Given the high sensitivity to initial conditions in chaotic systems and the impossibility of perfect initial states in experiments, reliable synchronization is crucial for applications like secure communications. To achieve this, a robust sliding mode control strategy based on three designed sliding surfaces is proposed to synchronize the master and slave systems. The designed sliding mode controller achieves excellent synchronization performance with a final synchronization error norm of || e || = 7×10 -6 and a convergence time 0.30 seconds. These quantitative results confirm the high precision and fast response of the proposed control scheme, making it suitable for practical synchronization application in fractional order systems. Following master-slave chaotic synchronization using the proposed scheme, this paper analyzes the secure message recovery performance through a practical scenario, specifically examining how output filter parameters impact the balance between effective noise mitigation and signal distortion. Numerical simulations confirm the effectiveness and robustness of the proposed control approach, demonstrating successful synchronization of the fractional-order Shimizu-Morioka system.