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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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