Complex conjugate matrix equations (CCME) are important in computation and antilinear systems. Existing research mainly focuses on the time-invariant version, while studies on the time-variant version and its solution using artificial neural networks are still lacking. This paper introduces zeroing neural dynamics (ZND) to solve the earliest time-variant CCME. Firstly, the vectorization and Kronecker product in the complex field are defined uniformly. Secondly, Con-CZND1 and Con-CZND2 models are proposed, and their convergence and effectiveness are theoretically proved. Thirdly, numerical experiments confirm their effectiveness and highlight their differences. The results show the advantages of ZND in the complex field compared with that in the real field, and further refine the related theory.

翻译：复共轭矩阵方程在计算和反线性系统中具有重要意义。现有研究主要集中于时不变情形，而针对时变情形及其利用人工神经网络求解的研究仍较为缺乏。本文引入归零神经动力学方法以求解最早的时变复共轭矩阵方程。首先，在复数域上统一定义了向量化与Kronecker积。其次，提出了Con-CZND1和Con-CZND2模型，并从理论上证明了其收敛性与有效性。再次，数值实验验证了模型的有效性并揭示了其差异。结果表明，与实数域相比，归零神经动力学在复数域具有优势，并进一步细化了相关理论。