With the increasing application of energy storage technology in microgrids, the stability of energy storage converters plays a critical role in the system’s performance. This paper proposes a hybrid automaton model for the Cuk topology energy storage converter, which unifies the system’s discrete and continuous states. Nonlinear analysis methods are employed to quantitatively analyze the dynamic behavior of the system under variations of key parameters. In buck mode, a Thevenin equivalent circuit model for the battery is introduced, incorporating the battery’s polarization effect into the system description, to analyze its influence on the system’s stability boundaries and bifurcation behavior. In boost mode, a multi-scale dynamic model is established by introducing parametric and external excitation, and the oscillatory behavior under three typical excitation frequency ratios is analyzed using the fast-slow dynamic analysis method. The results show that as the excitation frequency ratio changes, the structure of the system’s slow variables is altered, leading to the evolution of bursting oscillations from symmetric periodic bursting to asymmetric or multi-segment bursting forms. This study reveals the variation in the system’s dynamic response when parameters change, providing significant insights into the operational characteristics of the converter.

This paper introduces a novel color image encryption algorithm based on a five-dimensional continuous memristor hyperchaotic system (5D-MHS), combined with a two-dimensional Salomon map and an optimized Arnold transform. Firstly, convert the test image to a 2D pixel matrix then processed in blocks, and each block of the pixel matrix is permuted with chaotic sequences generated by 5D-MHS and 2D Salomon map. Then, the permuted image is permuted for three rounds with the optimized Arnold algorithm. Finally, one of the chaotic sequences generated by 5D-MHS is employed to diffuse the permuted image to obtain the final ciphertext image. In this paper, several pseudo-random sequences are generated and mixed in the permutation stage to achieve higher security. The algorithm achieves a key space of 2⁴⁷², the information entropy of the ciphertext image for the color image is 7.9998, number of pixels change rate (NPCR) and unified average changing intensity (UACI) reached 99.6131% and 33.4361%, respectively, and the correlation between pixels is close to 0. The simulation results show that the encryption algorithm is efficient and the key system is secure.

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.