Complex conjugate matrix equations (CCME) have aroused the interest of many researchers because of computations and antilinear systems. Existing research is dominated by its time-invariant solving methods, but lacks proposed theories for solving its time-variant version. Moreover, artificial neural networks are rarely studied for solving CCME. In this paper, starting with the earliest CCME, zeroing neural dynamics (ZND) is applied to solve its time-variant version. Firstly, the vectorization and Kronecker product in the complex field are defined uniformly. Secondly, Con-CZND1 model and Con-CZND2 model are proposed and theoretically prove convergence and effectiveness. Thirdly, three numerical experiments are designed to illustrate the effectiveness of the two models, compare their differences, highlight the significance of neural dynamics in the complex field, and refine the theory related to ZND.

翻译：复共轭矩阵方程因其在计算和反线性系统中的应用而引起了众多研究者的兴趣。现有研究主要集中于其时不变求解方法，但缺乏针对其时变形式求解的理论。此外，利用人工神经网络求解复共轭矩阵方程的研究尚少。本文从最早的复共轭矩阵方程出发，应用归零神经动力学求解其时变形式。首先，统一地定义了复数域中的向量化与克罗内克积运算。其次，提出了Con-CZND1模型与Con-CZND2模型，并从理论上证明了其收敛性与有效性。最后，设计了三个数值实验以说明两种模型的有效性，比较其差异，突出神经动力学在复数域中的意义，并完善了与归零神经动力学相关的理论。