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为了进一步提高混沌系统的复杂性，本文构建了一个新型四维忆阻超混沌系统，其中磁控忆阻器的存在提高了系统的复杂性，使其能够产生更丰富、更复杂的动态行为。所提出的系统有无数多个平衡点，产生的吸引子属于隐藏吸引子。我们讨论了随着参数变化系统的分岔行为、吸引子共存行为、瞬态现象、以及系统依赖于忆阻初始条件变化产生无限多共存吸引子的超级多稳定现象，分析表明新系统具有丰富的动力学行为。同时我们也分析了系统的不稳定周期轨道，建立了适当的符号编码，并探索了周期的修剪规则。此外，我们还提出了一种基于新的忆阻超混沌系统的数字图像加密方法，并验证其具有良好的加密效果。最后，利用 DSP 数字电路对新系统进行了实验验证，结果与数值仿真一致，验证了忆阻系统的正确性与可实现性。Memristors exhibit controllable nonlinear characteristics, generating chaotic signals that are characterized by randomness, sensitivity, and unpredictability, thereby demonstrating significant potential applications in information encryption and signal processing. With the integration of chaos theory and electronic technology, constructing memristive hyperchaotic systems has become a hot topic in nonlinear science and information security. This paper aims to overcome the limitation of monotonous dynamic characteristics in traditional chaotic systems by designing novel memristor-based hyperchaotic systems with richer dynamic behavior and higher application value. It conducts characteristic analysis, theoretical verification, application exploration, and hardware implementation to support its engineering applications. Building upon the classical Chen system, this work innovatively incorporates cubic nonlinear magnetically controlled memristor model as a feedback element. By establishing a mathematical model of the memristor and coupling it with the state equations of the Chen system, a four-dimensional memristor-based hyperchaotic system is designed. First, by integrating numerical computation with differential equation theory, a comprehensive mathematical model is established to analyze fundamental properties, such as symmetry and dissipativity, thereby validating the system’s rationality. Second, the system’s dynamical behaviors are analyzed, including attractor phase diagrams, Lyapunov exponents, power spectra, parameter effects, transient dynamics, and coexisting attractors. Simultaneously, variational methods are applied to analyze unstable periodic orbits within the system. A symbolic coding approach based on orbital characteristics is established to convert orbital information into symbolic sequences, and orbital pruning rules are explored to provide a basis for optimal orbital control. Furthermore, a digital image encryption method is proposed based on this system. Using chaotic sequences as keys, image pixels are scrambled and diffused. The effectiveness of encryption is validated through histogram analysis, correlation analysis, information entropy evaluation, and testing of anti-attack capabilities. Finally, a DSP-based digital circuit hardware platform is constructed to run the system, and researchers compare hardware experimental results with software simulation outcomes. Findings reveal that the introduction of memristors induces linearly distributed equilibrium points in phase space, generating hidden attractors that enrich the system’s chaotic behavior. Dynamic behaviors simulation confirm the rich dynamics of this four-dimensional memristorbased hyperchaotic system. The proposed digital image encryption method demonstrates robust security performance. The DSP hardware experiments and software simulations yielded highly consistent attractor phase diagrams, validating the system’s correctness and feasibility.
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