Dynamic Analysis and DNA Encryption of a Fractional‐Order Memristor Coupled With an HNN

ABSTRACT In this study, a fractional‐order memristor–coupled Hopfield neural network (HNN) system that comprises two identical neural networks interconnected via a voltage‐controlled memristor is proposed. By combining bifurcation diagrams, Lyapunov exponents, spectral entropy complexity analyses, phase portraits, and time‐domain plots, the unique coexisting and transient transition behaviors of this system were analyzed in detail. Furthermore, the transition from periodic to chaotic dynamics with varying coupling strengths can be assessed in detail. To validate the theoretical findings, an ARM‐based microcontroller was employed to implement the neural network system. The experimental results confirm the presence of different dynamic behaviors. By leveraging the inherent characteristics of the chaotic system, a DNA coding–based image encryption algorithm was designed. The results show that the system has high key sensitivity, large key space, good encryption performance, and anti‐interference performance.