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设计新型混沌系统能够丰富加密系统的候选资源，是基于混沌加密的安全性的重要途径。离散忆阻器因其固有的非线性特性与电路友好特性，为构建新型混沌系统提供了有效途径。然而，其在复值离散混沌系统中的应用仍有待探索。为此，本文构建了一种基于离散忆阻器的复高斯混沌模型，其中忆阻器由复数模长驱动。通过李亚普诺夫指数、分岔图和相图等数值仿真分析，验证了该系统具有增强的混沌特性。同时，在 FPGA 数字平台上实现了该模型的硬件部署，证明了其硬件可行性。基于该模型生成的复值混沌序列，本文进一步设计了一种双图像加密方案，将两幅图像视为复数矩阵的实部和虚部，通过混沌序列进行置乱和扩散操作。仿真结果表明，该加密方案具有高安全性，能够抵抗多种攻击。The exploration of complex-valued chaos offers a viable pathway not only for practical applications like image encryption but also holds significant potential for simulating wave phenomena and quantum inspired process. To bridge this with nonlinear circuit elements, we introduce a novel complex-valued chaotic system by embedding a discrete memristor into a complex Gaussian map. The memristor, a component with inherent physical memory, is uniquely driven by the modulus of the complex state variable, which is a key physical quantity often associated with energy or amplitude in wave systems. This coupling induces complex nonlinear dynamics, which are physically characterized through Lyapunov exponents and bifurcation analysis, revealing an enhanced and more robust chaotic regime. The physical feasibility of this system is demonstrated by its successful hardware realization on an FPGA platform. To showcase its application potential, we leverage the system’s complex chaotic steams to engineer a dual-image encryption scheme, where the encryption process is interpreted as a physical diffusion and scrambling of information represented by a complex matrix. Our results verify that this approach not only yield a cryptosystem with high security but also provide a link between complex chaos and information security applications.
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[1] Zhou S, Yin Y, Wang S, Zhang Y 2024 Acta Phys. Sin. 73 210501
[2] Bao H, Wang R, Tang H, Chen M, Bao B 2025 IEEE Internet Things J. 12 20902
[3] Deng Q, Wang C, Sun Y, Yang G 2025 IEEE Trans. Cybern. 55 3926
[4] Lai Q, Wang J, Huang D 2025 Acta Phys. Sin. 74 1
[5] Deng Q, Wang C, Yang G, Luo D 2025 IEEE Internet Things J. 12 25559
[6] Yu F, He S, Yao W, Cai S, Xu Q 2025 IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 44 1
[7] Zhou L, Lin Z, Tan F, Chen P 2025 Expert Syst. Appl. 281 127475
[8] Luo D, Wang C, Liang J, Deng Q 2025 Nonlinear Dyn. 113 1
[9] Chen W, Wang Y, Shi C, Shen G, Li M, Liu Y, Hei X 2025 Neural Netw. 191 107799
[10] Li H, Min F 2025 IEEE Internet Things J. 12 29018
[11] Bao H, Fan Z, Hua Z, Zhang Y, Xu Q, Bao B 2025 Expert Syst. Appl. 290 128448
[12] Wang X, Du J, Li Z, Ma M, Li C 2024 Acta Phys. Sin. 73 110503 (in Chinese) [王璇, 杜健嵘, 李志 军, 马铭磷, 李春来 2024 物理学报 73 110503]
[13] Yu F, Tan B, He T, He S, Huang Y, Cai S, Lin H 2025 Mathematics 13 726
[14] Zhang Y, Hua Z, Bao H, Huang H 2024 IEEE Trans. Circuits Syst. I 71 2783
[15] Hua Z, Yao J, Zhang Y, Bao H, Yi S 2025 IEEE Trans. Ind. Informat. 21 85
[16] Yao J, Zhang Y, Bao H, Hua Z 2025 Chaos, Solitons Fractals 197 116453
[17] Rani M, Agarwal R 2009 Chaos, Solitons Fractals 42 447
[18] Ayubi P, Barani M J, Valandar M Y, Irani B Y, Sadigh R S M 2021 Artif. Intell. Rev. 54 1237
[19] Yu Y, Ren S, Yang L, Li Y, Miao X 2025 Sci. China Inf. Sci. 68 139402
[20] Deng Q, Wang C, Sun Y, Xu C, Lin H, Deng Z 2025 IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 44 1
[21] Zhang X, Li C, Moroz I, Huang K, Liu Z 2025 Nonlinear Dyn. 113 15487
[22] Bao H, Fan J, Hua Z, Xu Q, Bao B 2025 IEEE Internet Things J. 12 31843
[23] Gao S, Ho-Ching Iu H, Erkan U, Simsek C, Toktas A, Cao Y, Wu R, Mou J, Li Q, Wang C 2025 IEEE Trans. Circuits Syst. Video Technol. 35 7706
[24] Al Qurashi M, Asif Q U A, Chu Y M, Rashid S, Elagan S K 2023 Results Phys. 51 106627
[25] Almatroud A O, Grassi G, Khennaoui A A, Abbes A, Ouannas A, Alshammari S, Albosaily S 2024 Alexandria Eng. J. 93 1
[26] Li H, Min F 2025 IEEE Trans. Circuits Syst. I 72 4820
[27] Wang C, Li Y, Yang G, Deng Q 2025 Mathematics 13 1600
[28] Yu F, Zhang S, Su D, Wu Y, Yumba Musoya G, Yin H 2025 Fractal Fractional 9 115
[29] Deng Q, Wang C, Sun Y, Yang G 2025 IEEE Trans. Circuits Syst. I 72 1
[30] Luo D, Wang C, Deng Q, Yang G 2025 Nonlinear Dyn. 113 28381
[31] Fan C, Ding Q 2025 Chaos, Solitons Fractals 191 115905
[32] Zhang S, He D, Li Y, Lu D, Li C 2025 IEEE Trans. Autom. Sci. Eng. 22 17828
[33] Yu F, Su D, He S, Wu Y, Zhang S, Yin H 2025 Chin. Phys. B 34 050502
[34] Zhang H, Fu C, Pan Z, Ding D, Wang J, Yang Z, Liu T 2024 Acta Phys. Sin. 73 108501
[35] Lai Q, Qin M 2025 J. Electron. Inf. Technol. 47 1 (in Chinese) [赖强, 秦铭宏 2025 电子信息学报 47 1]
[36] Lai Q, Qin M 2025 J. Guizhou Norm. Univ. (Nat. Sci.) 43 1 (in Chinese) [赖强, 秦铭宏 2025 贵州师 范大学学报 (自然科学版) 43 1]
[37] Lai Q, Wang J 2024 Acta Phys. Sin. 73 180503 (in Chinese) [赖强, 王君, 2024 物理学报 73 180503]
[38] Yu F, Yumba Musoya G, Guo R, Ying Z, Xu J, Yao W, Jin J, Lin H 2025 Axioms 14 638
[39] Zhao Q, Bao H, Zhang X, Wu H, Bao B 2024 Chaos, Solitons Fractals 182 114769
[40] An X, Liu S, Li X, Zhang J, Li X 2024 Expert Syst. Appl. 243 122899
[41] Zhong Y, Lai Q, Zhu C, Qin M 2026 Comput. Stand. Interfaces 95 104051
[42] Zhao Y, Zheng M, Zhang Y, Yuan M, Zhou H 2024 Nonlinear Dyn. 112 19515
[43] An T, Gao T, Chen T, Jiang D 2025 Complex Intell. Syst. 11 319
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