A novel five-term 3D chaotic system with two squared nonlinearities and its secure communication application for biomedical data

Abstract

Ensuring secure communication of biomedical data has become increasingly important due to its sensitive nature. Chaotic systems, with their inherent unpredictability and sensitivity to initial conditions, offer a promising approach for secure data encryption. This study introduces a novel five-term chaotic system that includes two squared nonlinearities, a unique configuration not previously reported in the literature. The system's dynamics are analyzed through equilibrium points, stability, bifurcation diagrams, and Lyapunov Exponents (LEs), where the Kaplan-Yorke dimension is found to be 2.1471 under selected parameters, confirming strong chaotic behavior. An electronic implementation of the system is achieved using standard analog components, validating its physical feasibility. The system is then applied to encrypt biomedical signals and images. In secure ECG signal transmission tests conducted on a Raspberry Pi, synchronization is achieved within 4 s using Sliding Mode Control (SMC). The encryption algorithm demonstrates high key sensitivity and a large key space. For biomedical image encryption, the proposed method achieves a Number of Pixels Change Rate (NPCR) of 99.56% and a Unified Average Changing Intensity (UACI) of 33.31%, indicating strong encryption performance. These results confirm that the proposed chaotic system is efficient, lightweight, and highly suitable for secure biomedical communication.