Dynamics analysis and image encryption application of a 3D chaotic system with a discrete memristor

Abstract

In this paper, a novel three-dimensional discrete memristive chaotic system is proposed. By embedding a single discrete memristor into a three-dimensional mapping structure, the system achieves hyperchaotic dynamics with a concise architecture. Theoretical analysis indicates that the equilibrium points of the system exhibit an evolution rule from a surface to a line and then to a point, which provides a structural foundation for multistability. Bifurcation diagrams, Lyapunov exponent spectra, and complexity analyses verify the hyperchaotic characteristics and rich multistable behavior of the proposed system. A ‘self-reproducing evolutionary structure’ is discovered, which is bounded in amplitude and topologically stable but continuously expands with iterations, offering a novel perspective on the evolution of chaotic dynamics. The dual sensitivity of the system to initial conditions provides a multi-dimensional key space for encryption applications. At the application level, an image encryption algorithm is designed, incorporating ‘plaintext perturbation + triple chained diffusion + triple dynamic permutation + adaptive rotation + XOR diffusion.’ Experimental results demonstrate that the ciphertext information entropy reaches 7.9994, the Number of Pixel Change Rate and Unified Average Changing Intensity are 99.6059% and 33.4910%, respectively, and the correlation coefficients are close to zero. Furthermore, the ciphertext change rate reaches 99.59% when the key changes by 10−15. Under 5% salt-and-pepper noise and 1/16 cropping attacks, the peak signal-to-noise ratio of the decrypted image reaches 25.3622 dB and 23.2575 dB, respectively, indicating that the algorithm possesses strong resilience against attacks. Additionally, the hardware implementation based on an STM32 microcontroller and a LabVIEW host computer validates the engineering feasibility of the system.