This paper delves into the synchronization dynamics of fractional-order memristor Cohen–Grossberg neural network systems with time-varying delays at predefined times (PTS-MFCGNNs). Firstly, leveraging the concept of predefined-time stability, we devise a fractional-order controller, establish sufficient conditions for predefined-time synchronization, and achieve synchronization within the Cohen–Grossberg drive–response system. Secondly, building upon these findings, we scrutinize the synchronization dynamics within the time domain of the PTS-MFCGNNs system. Finally, we validate our theoretical framework through numerical simulations and engage in a comprehensive discussion on predefined-time synchronization within the PTS-MFCGNNs system.

中文翻译：

---

基于忆阻器的时变延迟分数阶Cohen-Grossberg神经网络的预定义时间同步


本文深入研究了在预定义时间具有时变延迟的分数阶忆阻器 Cohen-Grossberg 神经网络系统 (PTS-MFCGNN) 的同步动力学。首先，利用预定义时间稳定性的概念，设计了分数阶控制器，为预定义时间同步建立了充分条件，并在Cohen-Grossberg驱动响应系统内实现了同步。其次，基于这些发现，我们仔细研究了 PTS-MFCGNN 系统时域内的同步动态。最后，我们通过数值模拟验证了我们的理论框架，并对 PTS-MFCGNN 系统内的预定义时间同步进行了全面的讨论。