Deng Quanli, Wang Chunhua, Sun Yichuang, Yang Gang
IEEE Trans Cybern. 2025 Aug;55(8):3926-3934. doi: 10.1109/TCYB.2025.3565333.
The randomness of chaotic systems are crucial for their application in secure communication. Conservative systems exhibit enhanced ergodicity and randomness in comparison to dissipative chaotic systems. However, the memristor-based conservative chaotic maps remain unreported. This article presents a study of volume-preserving chaotic maps based on discrete memristor (DM). We propose and analyze a generic conservative map that incorporates DM. The conservative characteristics of the proposed iterative map are confirmed through the determinant of its Jacobian matrix. Furthermore, four distinct DM models are introduced and their memristive characteristics are verified through numerical simulations of hysteresis loops. To investigate the dynamical properties of the discrete memristive conservative map (DMCM), we incorporate the proposed DM models into the generic conservative map model using numerical methods, including phase portraits, Lyapunov exponents, and bifurcation diagrams. Additionally, the hardware implementation of the DMCM on an FPGA platform demonstrates the reliability of the model. Finally, secure communication experiments based on the DMCM show that it outperforms some classical dissipative chaotic maps in terms of bit error rate performance.
混沌系统的随机性对于其在安全通信中的应用至关重要。与耗散混沌系统相比，保守系统表现出更强的遍历性和随机性。然而，基于忆阻器的保守混沌映射尚未见报道。本文提出了一种基于离散忆阻器（DM）的保体积混沌映射的研究。我们提出并分析了一种包含DM的通用保守映射。通过其雅可比矩阵的行列式证实了所提出的迭代映射的保守特性。此外，引入了四种不同的DM模型，并通过磁滞回线的数值模拟验证了它们的忆阻特性。为了研究离散忆阻保守映射（DMCM）的动力学特性，我们使用数值方法，包括相图、李雅普诺夫指数和分岔图，将所提出的DM模型纳入通用保守映射模型。此外，在FPGA平台上对DMCM进行硬件实现证明了该模型的可靠性。最后，基于DMCM的安全通信实验表明，在误码率性能方面，它优于一些经典的耗散混沌映射。
