The design of a chaotic image encryption algorithm plays an essential role in enhancing information and communication security. The performance of such algorithms is intricately linked to the complexity of the chaotic sequence and the underlying encryption algorithm. To additionally enhance the complexity of hyperchaotic systems, this study presents a novel construction of a Five-Dimensional (5D) memristive hyperchaotic system through the introduction of the flux-controlled memristor model. The system’s dynamic characteristics are examined through various analytical methods, including phase portraits, bifurcation diagrams, and Lyapunov exponent spectra. Accordingly, the sequences produced by the hyperchaotic system, which passed the National Institute of Standards and Technology (NIST) test, are employed to inform the creation of a novelty image encryption technique that combines hash function, Deoxyribonucleic Acid (DNA) encoding, logistic, and Two-Dimensional Hyperchaotic Map (2D-SFHM). It improves the sensitivity of key and plaintext images to image encryption, expands the algorithm key space, and increases the complexity of the encryption algorithm. Experimental findings and analysis validate the exceptional encryption capabilities of the novel algorithm. The algorithm exhibits a considerable key space 2⁵¹², and the ciphertext image demonstrates an information entropy of 7.9994, with inter-pixel correlation approaching zero, etc., showcasing its resilience against different types of attacks on images.

A fractional-order memristor load Buck-Boost converter causes periodic system oscillation, electromagnetic noise, and other phenomena due to the frequent switching of the switch in actual operation, which is detrimental to the stable operation of the power electronic converter. It is of great significance to the study of the modeling method and chaos control strategy to suppress the nonlinear behavior of the Buck-Boost converter and expand the safe and stable operation range of the power system. An estimation-correction modeling method based on a fractional active voltage-controlled memristor load peak current Buck-Boost converter is proposed. The discrete numerical solution of the state variables in the continuous mode of the inductor current is derived. The bursting oscillation phenomenon when the system introduces external excitation is analyzed. Using bifurcation, Lyapunov exponent, and phase diagrams, a large number of numerical simulations are performed. The results show that the Buck-Boost converter is chaotic for certain selected parameters, which is the prerequisite for the introduction of the controller. Based on the idea of parameter perturbation and state association, a three-dimensional hybrid control strategy for a fractional memristor Buck-Boost converter is designed. The effectiveness of the control strategy is verified by simulations, and it is confirmed that the system is controlled in a stable periodic state when the external tunable parameter s, which represents the coupling strength between the state variables in the system, gradually decreases in [−0.4, 0]. Compared with integer-order controlled systems, the stable operating range of fractional-order controlled systems is much larger.