A novel 4D chaotic system coupling with dual-memristors and application in image encryption

A novel 4D dual-memristor chaotic system (4D-DMCS) is constructed by concurrently introducing two types of memristors: an ideal quadratic smooth memristor and a memristor with an absolute term, into a newly designed jerk chaotic system. The excellent nonlinear properties of the system are investigated by analyzing the Lyapunov exponent spectrum, and bifurcation diagram. The 4D-DMCS retains some characteristics of the original jerk chaotic system, such as the offset boosting in the x-axis direction. Simultaneously, the integration of the two memristors significantly enriches the dynamic behavior of the system, notably augmenting its transitional behaviors, fostering greater multistability, and elevating both spectral entropy and C0 complexity. This augmentation underscores the profound impact of the memristors on the system's overall performance and complexity. The system is implemented through the STM32 microcontroller, further proving the physical realizability of the system. Ultimately, the 4D-DMCS exhibits remarkable performance when applied to image encryption, demonstrating its significant potential and effectiveness in this domain.