Traditional low dimensional chaotic maps suffer from limited dynamical complexity and weak randomness, reducing their effectiveness in applications. This paper presents a general framework for constructing 4-D memristive hyperchaotic maps, from which four representative hyperchaotic maps are developed. These maps exhibit diverse dynamical behaviors. Importantly, all four maps are designed without fixed points due to the inclusion of two oscillatory terms. By adjusting the internal memristor state, they generate infinitely many coexisting attractors, and they further enable controllable amplitude modulation as well as parameters driven attractors offset boosting. A digital hardware platform is developed to implement the proposed maps and experimental results demonstrate their robustness and feasibility in embedded environments. An image encryption algorithm based on it is designed, results exhibiting robust resistance against brute-force attacks, diverse noise attacks at varying intensities, cropping attacks and differential cryptanalysis.

Constructing memristive neural networks (MNNs) with multiscroll chaotic attractors helps advance both theoretical and applied research on neural networks. However, the existing models mainly utilize complex memristor models with polynomial functions, nested composite functions, and so on, to generate multiscroll chaotic attractors, which leads to increased model complexity and difficulties in on-demand adjustment. Hence, this article proposes a reconfigurable multiscroll MNN (RMMNN) that can yield different types of multiscroll chaotic attractors merely by altering the memristive parameters without modifying its model. Through numerical methods, the complex dynamics of the RMMNN in different cases are analyzed, such as parameter-controlled multiscroll chaotic attractors, adjustable multistability, and parameter-induced transitions of multistability. In addition, the reliability of the numerical analysis is verified via the hardware circuits. Moreover, to address the issues of image security and low quality in telemedicine, a bidirectional rotation medical image encryption scheme (BRMIES) is developed based on the good pseudorandom chaotic sequences generated by RMMNN. Performance analysis demonstrates that BRMIES can effectively protect medical image and robustly handle various potential adverse interferences within telemedicine process.

With consideration of the inherent nonlinearity and distinctive memory characteristics, memristors are excellent candidates for constructing multiscroll attractors. This paper seeks to introduce a memristor into the Chua’s circuit to operate in conjunction with a novel piecewise nonlinear resistor which replaces the Chua’s diode to design the circuit that can generate grid multiscroll attractors, which is designated as multiscroll memristive Chua’s circuit (MMCC). The designed MMCC is capable of generating any number of scrolls, with the number of scrolls expanding in accordance with the internal variables of the memristor and the nonlinear resistor. By utilizing phase portraits, bifurcation diagrams, Lyapunov exponents (LEs), coexisting attractors and amplitude modulation thoroughly examined its property. The feasibility of the MMCC is demonstrated through circuit implementation. Furthermore, we design the predefined-time synchronization (PTS) controller for the MMCC, serving as the foundation for a multi-channel segmented secure communication scheme, whose effectiveness is rigorously validated through experimental testing.