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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.
Lai et al. (Fri,) studied this question.