In this article, we investigated a class of genetic regulatory networks (GRNs) with time-varying delays and Stepanov-like weighted pseudo-almost automorphic coefficients. By Banach fixed point theorem, we firstly established the existence results of the weighted pseudo-almost automorphic solutions for the proposed GRNs. Secondly, by using suitable Lyapunov functional and mathematical analysis skills, new criteria are derived for ensuring the global exponential stability of the solutions. Finally, a numerical example and remarks are provided to substantiate the efficiency of obtained results. The derived results of this article are new and complement many earlier works and the ideas of this work can be applied to investigate other similar systems.

在本文中，我们研究了一类具有时变时延和类Stepanov加权伪几乎自同构系数的遗传调控网络（GRN）。通过Banach不动点定理，我们首先建立了所提出的GRN的加权伪几乎自同构解的存在性结果。其次，通过使用适当的Lyapunov函数和数学分析技能，可以导出新的准则来确保解决方案的全局指数稳定性。最后，提供了一个数值示例和说明以证实所获得结果的效率。本文的衍生结果是新的，是对许多早期工作的补充，并且该工作的思想可用于研究其他类似的系统。